Here's a recent book that I purchased and highly recommend:
Evidence Matters - Science, Proof and Truth in the Law (2014, Cambridge U. Press) by
Susan Haack, one of my favorite female philosophers.
https://www.amazon.com/Evidence-Matters-...ref=sr_1_1
Here's Amazon's book-blurb:
"Is truth in the law just plain truth - or something sui generis? Is a trial a search for truth? Do adversarial procedures and exclusionary rules of evidence enable, or impede, the accurate determination of factual issues? Can degrees of proof be identified with mathematical probabilities? What role can statistical evidence properly play? How can courts best handle the scientific testimony on which cases sometimes turn? How are they to distinguish reliable scientific testimony from unreliable hokum? The dozen interdisciplinary essays collected here explore a whole nexus of such questions about science, proof, and truth in the law."
Susan Haack writes:
"The mathematical calculus of probabilities is perfectly fine
in its place, but that place is a limited one. In particular, this mathematical calculus sheds little or no light on the crucial concept Russell calls "rational credibility" and I call "warrant". One consequence, as I shall argue here, is that we can't look to probability theory for an understanding of degrees and standards of proof in the law, but must look, instead, to an older and less formal branch of inquiry: epistemology."
Considering the prison population in just 1992 was around 900,000, 362 wrongful conviction since 1992 isn't really on the level of crisis. Probability and statistics are just as incomprehensible for most jurors, if not more so, than forensic evidence. A "defense hypothesis" would seem to play into the TV notion that the defense should somehow manage to do the job of the police and find the guilty party. So that would seem to be an end-around on a presumption of guilt...where the onus lies with the defense. A prosecutor's argument, without evidence, is not compelling, and there is no evidence for a null hypothesis (the defense saying something did not happen). There is also a heuristic that involves the interaction of evidence independent of any one individual likelihood ratio.
Legal truth/proof is definitely a different animal altogether from truth in general. It engages with moral intuitions and natural biases most people are not versed in dissecting.