It seems to me that the prosecution's case against Sollecito relies quite heavily on the evidence they claim proves he was present at the crime scene since they have no other solid evidence against him.

The reasoning used by the prosecution is basically what Jaynes calls the 'policeman's syllogism' in Probability Theory: The Logic of Science. The reasoning is of the form:

• If A is true, then B becomes more plausible
• B is true
• Therefore, A becomes more plausible

Here A is (Sollecito was present at the crime scene) and B is (DNA tests on the bra clasp detected Sollecito's DNA). If we use C to stand for our background knowledge then by Bayes theorem:

p(A|BC) = p(A|C) * (p(B|AC) / p(B|C))

The premise of the policeman's syllogism "If A is true, then B becomes more plausible" takes the form

p(B|AC) > p(B|C)

And by Bayes theorem if this premise is true then:

p(A|BC) > p(A|C)

as stated in the syllogism. Now the significance of the evidence B depends on the magnitude of p(B|C) - the only way finding B to be true can greatly increase the plausibility of A is if p(B|C) is very small relative to p(B|AC). In other words, the prosecution's argument rests on the background probability of finding Sollectio's DNA on the bra clasp being very low relative to the probability of finding it if he were present at the crime scene.

Now it seems to me that the fact that the DNA of several other unidentified individuals (who it is not suggested were present at the crime scene) was also found on the bra clasp indicates that p(B|C) is not so much smaller than p(B|AC). B is only strong evidence for A if DNA on the clasp is much more likely if the person was present at the crime scene but we have several counter examples of DNA on the clasp from individuals who were not at the crime scene so we have reason to doubt that p(B|AC) is much greater than p(B|C) and therefore reason to doubt the significance of the evidence.