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janos comments on Rationalists should beware rationalism - Less Wrong
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The rational way to establish the probability of a hypothesis is by testing it.
If a hypothesis is untestable in principle then its probability is zero, or undefined if you prefer. There's no way to assign any probability to it.
If it's impractical to test a hypothesis--e.g. if it would cost a trillion dollars to build a suitable particle accelerator--then the hypothesis stays in limbo until its proponents figure out a test to perform. At some point a probability can be assigned to it, but not yet.
Either way, if you're using "likeliness" to mean "probability" then it seems to me that testable hypotheses are "more likely" than untestable ones--insofar as we assign a probability to one and assign no probability to the other. If Bayes's Theorem keeps returning "undefined", you're doing it wrong.
Bayes' Theorem never returns "undefined". In the absence of any evidence it returns the prior.
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.
Solomonoff induction. Presumably you agree the probability is less than .1, and once you've granted that, we're "just haggling over the price".
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.