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But, of course, the mathematics of probability theory don't work that way. A hypothesis, such as that the apparent burglary in Filomena Romanelli's room was staged -- doesn't get points for its ability to explain the data unless it does so better than its negation. And, in the absence of the assumption that Knox and Sollecito are guilty -- if we're presuming them to be innocent, as the law requires, or assigning a tiny prior probability to their guilt, as epistemic rationality requires -- this contest is rigged. The standards for "explaining well" that the fake-burglary hypothesis has to meet in order to be taken seriously are much higher than those that its negation has to meet, because of the dependence relation that exists between the fake-burglary question and the murder question.
This isn't quite true. If the prior probability of being a murderer is 1 in 10^6, and I can find 30 things that are explained twice as well by the murder hypothesis as the non-murder hypothesis, then the posterior probability of being a murderer is 99.9%, in the absence of mitigating factors (since 2^30/10^6 is about 1000.) So, many pieces of weak evidence for an unlikely proposition can still establish that proposition.
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I began with zero familiarity with the case.
Rationale for considering Sollecito more likely than Knox: They're linked quite closely here, but there's enough confusion surrounding the case that I can't take that completely for granted. That being the case, it's unlikely-but-possible that one of Knox or Sollecito was directly involved while the other wasn't, and my prior for a male committing a violent rape/murder is a lot higher than for a female.
Guede is clearly guilty. He fled town immediately after the murder. His DNA was found in the victim's body, by far the most difficult-to-contaminate piece of DNA evidence in the case, making it extremely likely he's the rapist. Very low prior on a rape/murder being committed by separate parties.
The inconsistencies in Knox and Sollecito's stories are definitely worth paying attention to. But there are several factors diluting their importance:
The DNA evidence against Knox and Sollecito is also worth paying attention to, and is in fact the primary reason my estimate on their guilt is as high as it is. However, this is partially mitigated by a glaring problem with the case: Most of the evidence was collected before Guede was a suspect. If Guede had been identified from the start, the Knox-Sollecito hypothesis may not have been quite so "privileged". IIRC, the DNA of four unidentified individuals was also found on the knife. Plus the doubt wrt the knife matching the wounds. Plus the odds that Sollecito would take a murder weapon back to his apartment and put it away. My generally unfavorable prior wrt Italy's justice system also adds a fair amount of room for uncertainty here.
The fact that Guede wasn't initially identified also provides the police with a mild motive for contaminating the evidence. It's unlikely that such an action would be detected. That said, my prior for this sort of action is pretty low.
Finally, we come to the elephant in the case: The hypothesis that the murder was committed by three people working together, as the result of a sex game gone bad. This reads like a parody of a flailing prosecutor. Contrast prior with that for a "normal" rape/murder... ouch. And it just so happens that the one party implicated by actual, solid evidence is the one party who fled after the crime.
The rationale for my 80% chance of agreement with komponisto is mostly based on "metagaming" his position. He admits to having a "rather strong" opinion on the case, and it seems much, much harder to form a strong opinion in favor of guilt as opposed to innocence in this case. My estimate would be higher, but given how asymmetrical this case appears to me, I can't rule out "initial counterintuitiveness" and/or extra evidence as a possible motivation for posting this in the first place.
I'll read the other comments and post my update later today.
The facts as presented are not accurate so that is throwing off your calculation.
For example, when discounting Knox's statement to the police most people consider that it was after a length interrogation but the truth is the questioning lasted one hour. They accept that Knox was mistreated but all the evidence points to them treating her toughly but as expected for a murder suspect. What is never mentioned in the interrogation story is that Sollecito told the police Knox was not with him the night of the murder and that he lied at Knox's request. This information was in fact what led to Knox placing herself at the crime and accusing an innocent man. It should also be noted that this is the second innocent black man Knox had tried to implicate.
Also missing from consideration is the fact that Luminol revealed footprints matching both Amanda Knox and Raffaele Sollecito’s feet in the corridor between Knox’s room and the victim’s room and nowhere in the house. The prosecution advanced the theory that these were made by the accused in the victim’s blood while the defense presented the argument that these could have been made at a different time. When one of the footprints contained both Knox and victim’s DNA the expert argued independent deposit.
These are not equivalent explanations. The defense position requires that there be a reason for Knox and Sollecito to have blood on their feet. No such reason was ever given but since they had dated for less than two weeks if such an event had occurred it certainly would have been fresh in everyone’s memory. So not only does it require that there be an occurrence unrelated to the murder where these footprints were made but further both Meredith and Amanda had to deposit DNA presumably by spitting of some kind of nasal discharge in the exact same spot. We should also add a reason for why these prints only appear between the victim’s room and Knox’s room and not in the rest of the corridor. That or we accept the obvious that they were made the night of the murder in the victim’s blood.
Then there is a series of other evidence missing from the Wikipedia article. No mention of Knox lying to the police to delay the discovery of the body. No mention of Knox going from a state of joking around to hitting herself repeatedly when asked to provide her fingerprints for exclusionary purposes. No mention of Knox’s story not matching the evidence of what happened November 2. So yes if you remove all the evidence and change what you even bother to mention then Knox and Sollecito are innocent but that is not reality. If you want the real evidence I would suggest you read here http://themurderofmeredithkercher.com/ everything is sourced to primary sources and there is next to no opinion. Just the facts. See if you still feel the calculation comes out as not guilty.