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Annoyance comments on Rationalists should beware rationalism - Less Wrong
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Bayes' Theorem is undefined if p(X) is undefined.
Suppose our untestable-in-principle hypothesis is that undetectable dragons in your garage cause cancer. Then X is "undetectable garage dragon." As far as I can tell, there is no way to assign a probability to an undetectable dragon.
Please correct me if I'm wrong.
What's wrong with zero? An indetectable something is redundant and can be eliminated without loss; it has no consequences that the negation of its existence doesn't also imply. You might as well treat it as impossible - if you don't like giving zero probabilities, assign it whatever value you use for things-that-can't-occur.