an AI with a prior of zero for the existence of the outside world will never believe in it, no matter what evidence it sees.

Would such a constraint be possible to formulate? An AI would presumably formulate theories about its visible universe that would involve all kinds of variables that aren't directly observable, much like our physical theories. How could one prevent it from formulating theories that involve something resembling the outside world, even if the AI denies that they have existence and considers them as mere mathematical convenience? (Clearly, in the latter case it might still be drawn towards actions that in practice interact with the outside world.)