[wasabi991011]

Deciding that they are both equally likely is also a deciding a prior.

Yes, "equally likely" is the minimal information prior which makes it best suited when you have no additional information. But it's not unlikely that have some sort of context you can use to decide on a better prior.

[usgroup]

Well that would be extra information. Wherever you find the edge of your information, you will find the "problem of induction" as presented above.