Under uncertainty, precise probability cannot be assigned, see my other question: How valid is assignment of probabilities when evidence is totally lacking, as in Pascal's Wager? In this case, either probability cannot be assigned, or a range of probabilities is assigned (in the case of complete uncertainty, [0, 1]).
How does this change when there is some evidence, but not full evidence? For example, many cosmologists posit the existence of an infinite universe under the assumption that the universe is flat. This does not directly follow, yet many physicists say that it is "likely."
In general, how can evidence slightly favoring one hypothesis over another be used in support of that hypothesis, if the prior probability of the hypothesis being true is not known? Indeed, if we have a probability ranging over [0, 1], and any value can rationally be chosen from that, we could choose 1. This makes evidence useless in support or refutation of that hypothesis, according to Bayes' Theorem.
Question: In what sense can we use evidence to change our probabilities of a given proposition if the prior probability of that proposition cannot be known (or range over an interval)?