Also I would say people don't like probabilistic arguments used in justice. Punishing someone for a high probability that they did something, feels very unfair. But in this universe, this is all we can have.

Would it feel fair to imprison someone because there is a 50% probability they did something wrong? How about 80%? 90%? 99%? People like to pretend that there are some magical values called "reasonable doubt" and "beyond a shadow of doubt" where probabilities stop being probabilities and become a separate magisterium.

We are not good at dealing with probabilities and what we intuitively seek is probably a social consensus -- if everyone important thinks the guy is guilty, then it is safe to punish him. We are trying to be more fair than this, and partially we are succeeding, and partially we are trying to do the impossible, because we can never get beyond probabilities. But there are huge inferential gaps that prevent explaining this in the court.