Depends on the context. In the general, abstract case, you end up talking about things like ignorance priors and entropy maximization. You can also have sets of priors that penalize more complex theories and reward simple ones; that turns into Solomonoff induction and Kolomogorov complexity and stuff like that when you try to formalize it.

In actual, practical cases, people usually try to answer a question that sounds a lot like "from the outside view, what would a reasonable guess be?". The distinction between that and a semi-educated guess can be somewhat fuzzy. In practice, as long as your prior isn't horrible and you have plenty of evidence, you'll end up somewhere close to the right conclusion, and that's usually good enough.

Of course, there are useful cases where it's much easier to have a good prior. The prior on your opponent having a specific poker hand is pretty trivial to construct; one of a set of hands meeting a characteristic is a simple counting problem (or an ignorance prior plus a complicated Bayesian update, since usually "meeting a characteristic" is a synonym for "consistent with this piece of evidence").