Question

Why is knowledge with a high probability a more valid tool for decision-making than a bet with a high probability?
In other words, why does it make sense for a judge to convict a person on the basis of witnesses who were in the area (where there is a small chance that they confused him with someone else or simply made it up), but not on the basis of a probabilistic bet? For example, there is a group of prisoners who beat up a guard, while one prisoner tried to stop them. For each individual prisoner, there is a high probability that he was among those who beat the guard. Suppose the probability of each individual prisoner being part of the group that beat the guard is equal to the probability that the witnesses in the first example I gave were mistaken or fabricated their testimony. Why does it make a difference that in the second case the decision was made through a probabilistic bet, while in the first case the decision was made under highly probable knowledge?