You are absolutely correct.

I should have said "anything of this nature", my mistake.

This seems like ridiculous hyperbole - science has far more ability to "prove" things that are repeatable than unrepeatable.

You are completely correct.

In the spirit of constructing the best possible argument to engage with, I think we should run as if bigjeff5 had actually said exactly what he said, but appended to it "and the prior probability of the alleged crime having occurred as per the police theory is so incredibly low that nothing but physical evidence that Knox and Sollecito were involved in the murder should push our posterior probability into the >1% range", or something similar.

I want to print this comment out and frame it. This is for real, not tongue in cheek irony?

Since the elimination of the faulty DNA evidence (which was previously the best evidence against them), the best evidence against Knox and Sollecito come from the police interrogation, specifically Knox's confession, and the fact that they knew the victim.

The strongest bit here is the confession, as knowing the victim is, at best, a pointer for where to look for a suspect - it is incredibly weak evidence on its own (in fact, there are dozens of people who fit better based on just knowing the victim) and does not in any way eliminate the possibility of a random stranger committing the crime. By all accounts the three got along reasonably well, if not particularly friendly to each other.

There are some interesting facts about the confession that I think you're missing:

1.) It is factually incorrect. The statements in the confession do not fit the facts of the crime. This severely damages the validity of the confession.

2.) The confession came after 24 hours of non-stop interrogation by the Italian police. There have been a number of studies that have shown that suspects become highly confused after long, intense interrogation sessions - particularly those that include sleep deprivation as was the case here. Suspects can be coerced into making whatever statements the interrogators want. In fact, in the US we have laws against this kind of treatment, including things like the right to silence and the right to have an attorney present during an interrogation to prevent exactly these scenarios. As an attorney I'd expect to know this.

Taken together, by far the most likely scenario is that the police coerced the confession out of Knox. Just on the facts relating to the interrogation alone, I'd put the likelihood that the confession was genuine at 10% at the very highest.

If the confession were genuine, we would expect some physical evidence of Knox and Sollecito at the crime scene. Given the fact that there is literally zero physical evidence of Knox and Sollecito's involvement, the likelihood that the confession is genuine must drop even further, to below 1%.

Considering the confession is about the only evidence for their involvement, I have to place the likelihood of their guilt at <1%. (There was a homeless man who claimed he saw them enter the apartment, but this is so weak as to be irrelevant given the poor track record of eyewitness accounts even immediately after a highly memorable event, the credibility of a detailed recollection of a mundane event over a year after it occurred is virtually non-existent, particularly without any evidence to back it up of any kind.)

Also, the reason I suggested you re-read the sequences is because you stated that you were 90% certain that all three were guilty, yet 90% that Guide was guilty even if the other two were not. This is a major failure in probability (and is actually a pretty common bias), as the options are Guide acted alone, or Guide acted with accomplices. Eliminating Knox and Sollecito from the equation eliminates a point of uncertainty, no matter how certain you are of Knox and Sollecito's guilt, and aught to increase your confidence in the individual assessment of Guide's guilt. Being 99% certain that Guide is guilty, and 90% certain that Guide, Knox, and Sollecito are guilty is logically consistent. Being 90% certain that Guide is guilty, yet 90% certain that all three are guilty is not logically consistent. You have to either lower you confidence in the guilt of all three, or raise your confidence in the guilt of Guide.

I may have phrased that last paragraph poorly, but most people should be able to understand it. I may edit for clarity later.

Edited to add: Here is a good article on coerced confessions, written by a forensic scientist.

Second edit, sorry, pertinent quote from the article:

When a confession is admitted and later retracted and claimed to have been made under duress, an additional question is whether the jury can understand the pressures that led up to the confession. Milgram's (1963, 1964) obedience studies suggest that, although most people may believe they personally would never succumb to pressure, their behavior in a coercive environment is to conform. Jury members may be unable to perceive how an innocent person could actually confess to something he did not do. Widespread overconfidence in personal ability to resist coercion may lead jurors to give undue and erroneous weight to a coerced confession. Expert testimony may be necessary to help jurors understand the circumstances that lead to nonvoluntary confessions, but trial courts have not always admitted such testimony.

What do you think are some of the best pieces of evidence against Knox and Sollecito?

Honestly, given what I know about the facts, the strongest evidence of guilt is that Knox and Sollecito were roommates of Knox.