Some people say that zero is not a probability :-)
But yes, if you have completely ruled out Z as impossible, you will not consider it any more and it will be discarded forever.
Unless the agent can backtrack and undo the inference chain to fix its mistakes (which is how humans operate and which would be a highly useful feature for a fallible Bayesian agent, in particular one which cannot guarantee that the list of priors it is considering is complete).
But if the probability ever goes to zero, it stays there.
Some people say that zero is not a probability :-)
But yes, if you have completely ruled out Z as impossible, you will not consider it any more and it will be discarded forever.
Unless the agent can backtrack and undo the inference chain to fix its mistakes (which is how humans operate and which would be a highly useful feature for a fallible Bayesian agent, in particular one which cannot guarantee that the list of priors it is considering is complete).