There's this Minecraft speed-runner called Dream who has been accused of cheating due to his drop luck (ie receiving useful things in the game). A moderator team has calculated that the p-value of the chance you'd get the same drops as Dream just by chance is in the magnitude of 10^-12. So, the moderator team concluded that Dream was cheating, and so did many others.
However, isn't this an argument from personal incredulity? There's a nonzero probability that Dream just got lucky and wasn't cheating, even if the probability is very small. This means that people think Dream is cheating just because they can't believe he got that lucky, so isn't that a personal incredulity argument?
I also think that it is obvious that Dream is cheating, but I do not know whether this proof is rigorous or not.