I was doing a bit of thinking based on the LessWrong article linked to previously, and the demands that the burglary, knife etc... need to be proved beyond reasonable doubt.
Say you have a bunch of individual, independent claims, "the burglary was faked" for example, each of which, if true make the claim "Amanda and Raffaele committed the murder" true.
If the odds of each of the claims being true is 0.3333... I think the odds of "Amanda and Raffaele committed the murder" being true is greater than .95 if you have 7.4 such sub claims. If the odds of the sub claims being true is 0.5, then you need 4.32 subclaims.
Clearly this is simplistic and the defense has similar claims, like the alibi, which would need to be factored in, and in any case there are other problems like what odds to assign, what defense/prosecution claims to include and exclude..... My purpose in posting was to underline the fact that the individual elements of the case, whether supporting the defense or the prosecution, don't even have to be better than 50% probable to provide support for a case.
The problem I see with this type of logic is the claims are not independent so the math is not as simple as you lay out. You need to consider the correlation between the events (if break-in was real, then likelihood of knife being contamination is increased or vice-versa).