Say there is a criminal who confesses to a crime, and quite obviously did it, but the police failed to properly Mirandize them, or otherwise unlawfully elicited the confession. Legally, you should find them not guilty

That's a separate matter entirely. (Actually, my understanding of the way it's supposed to work in such a case is that you're not supposed to ever hear about the confession as a juror, and so may not have enough evidence to rationally believe they're guilty with the required confidence, even if they in fact are; as opposed believing them guilty beyond a reasonable doubt, but just "finding" them not -- a form of jury nullification.)

This discussion here is entirely about one's rational belief about guilt or innocence, not anyone's legal opinion on the admissibility of evidence into court. You said your probability estimate that Amanda Knox killed her roommate was 15%. That's the information of interest, and it makes you a firm innocentista. Legal issues are a red herring. They would be a red herring even if your belief was 75% -- but in that case, it would at least be a legitimate discussion point to say,"thus, although I believe she probably did it, I would have to acquit if I were on a jury, because I don't believe it beyond a reasonable doubt."