If you haven't the faintest clue whether some proposition p is true or false, what subjective probability (credence) should you give it? 1/2? A common answer these days is that you shouldn't give it a precise credence at all. Instead, your credence should be spread over an interval, such as [0,1]. Greater precision than that ought to be based on real knowledge, e.g. of objective probabilities. Mere ignorance doesn't qualify one to make such claims.
Roger White, in his talk 'Evidential Symmetry and Mushy Credence', offers a neat argument for the old-fashioned answer of 1/2,* which goes roughly as follows:
Coin Game: Suppose you're given a fair coin which has 'p' plastered on one side, and '~p' on the other. Moreover, you know that whichever one is true was plastered over the Heads side. You toss the coin and it happens to land on 'p'.
(1) It's a fair coin, so you should initially give P(heads) = 1/2.
(2) This should not changed upon seeing the coin land on 'p' -- you have no idea whether p is the true one or not, so there is no new evidence for you here. So your updated P+(heads) = initial P(heads) = 1/2.
(3) Since the coin landed on 'p', this will be heads-up iff p is true. Hence P+(p) = P+(heads) = 1/2.
(4) But the coin landing on 'p' doesn't tell you anything new about the proposition's truth value. So your prior credence P(p) should also have been 1/2.
* Correction: the argument merely shows that your credence in p shouldn't be imprecise (for that entails, contradictorily, that it should be precisely 1/2). Maybe it should be some other precise value, though; that will depend on the details of what proposition p is.