According to subjective Bayesianism, the only constraints on prior probabilities are that they be consistent and, for contingent events, strictly between 0 and 1. But this makes it too easy to be within one's full epistemic rights in believing really silly stuff with no evidence whatsoever, just by having assigned it a high prior.
Perhaps what the subjective Bayesian needs to do is distinguish epistemic permissibility, which one can have without evidence, from epistemic justification, which requires some evidence. I doubt that the subjective Bayesian is going to be able to run a good story here that's consistent with the subjective elements. After all, there are many silly things that we are justified in disbelieving precisely because of their low priors and despite there being evidence for them, such as the law of gravity that says F=Gmm'/r2+a, where a=10−1000000, a law that we actually have a lot of evidence for—any evidence we have for Newton's law of gravitation is also evidence for this law, since the two laws are experimentally indistinguishable—but which we rightly disbelieve precisely because of low priors.
The Bayesian needs non-subjective priors.