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JoshuaZ comments on Causal Universes - Less Wrong
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No. This isn't conservation of expected evidence but a simple consequence of Bayes theorem. If your prior probability is zero, then you end up with a zero in the numerator of the theorem (since P(A) is zero). So your final result is still zero.
Of course, if you also assigned a probability of zero to the event you just observed, now you have 0/0 error, which is more awkward to deal with. The case of having a posterior probability of zero in contradiction to the evidence is not particularly problematic for the agent's thinking, it just isn't very useful. But a true 0/0 event might well cause serious issues.
In practice, you conclude you hallucinated the event.