Prior probability is what you can infer from what you know before considering a given piece of data.
If your overall information is I, and new data is D, then P(H|I) is your prior probability and P(H|DI) posterior probability for hypothesis H.
No one says you have to put exactly 0.5 as prior (this would be especially absurd for absurd-sounding hypotheses like "the lady next door is a witch, she did it".)
If we distinguish between "previous information" and "new information", than yes. In this case, the OP made no such distinction, so I can only assume his use of "prior" means "previous to all information we know" (I is nothing - an uninformative prior).
By the way, I don't really see a problem with starting with a prior of 0.5 for "the lady next door is a witch" (which could be formalized as "the lady next door has powers of action at a distance that break the laws of physics as we know them") - mo...
Could you use Bayes Theorem to figure out whether or not a given war is just?
If so, I was wondering how one would go about estimating the prior probability that a war is just.
Thanks for any help you can offer.