Question: What level of proof is required for conviction of crime?
Answer: Proof beyond a reasonable doubt.
Question: Does a showing of a "strong probability" of criminal guilt constitute proof beyond a reasonable doubt?
Answer: Under some circumstances.
Question: Under what circumstances?Except to the extent that the Court acknowledges that probabilities (of some kind and in some way) can figure in the trier's assessment of criminal guilt, the Court's reasoning has an Alice-in-Wonderland air:
Answer: When the probability is so strong that it excludes reasonable doubt.
"It's all very clear, my dear: Proof beyond a reasonable doubt is proof that removes all reasonable doubt. Why are you troubled by this self-evident proposition?"
It's here: the law of evidence on Spindle Law. See also this post and this post.