Statistics say he did it, Do you convict?

The problem with the example in the OP is that it assumes a level of knowledge in criminology that’s far, far above the level that actually exists. Indeed, it’s far from the level that could ever exist, unless not just the accuracy of criminology improves but society itself changes in some weird way. There are no comparable crimes at present for which one could say that if crime X happens then Y (who is in relation Z to the victim) must with probability 99% or greater be the criminal. There are, I suppose, cases like the following: A woman is found murdered. Her estranged husband was known to be violent. Now, any competent detective is going to immediately suspect the husband. He may even, if he thinks in a mathematical way, say that in cases like this 10% or 25% or 40% of the time it does turn out to be the husband. It’s not anywhere close to 100% of the time though. He’s not going to immediately bring the case to a grand jury though. He’s not even going to declare the husband to be the prime suspect, I think, but just a person of interest. He’ll go and interview the husband and find out if he has an alibi. He’ll go to the murder scene and find if there’s any evidence that points to anybody specific being the murderer.

I can’t think of any crime for which a criminologist could say with 99% accuracy that a person with a specific relationship must have done the crime. Even if there was such a crime, 99% accuracy isn’t enough to convince a jury, I think. The problem with the situation proposed in the OP isn’t that the case relies on probabilities. All court cases rely on probabilities. Even if a jury votes to convict, they realize that there is a tiny chance that they may be wrong. The problem is that criminology doesn’t have the accuracy that you posit and as far as I can see will never have that accuracy.