A wise person once said (emphasis -- and the letter c -- added):

"Uncertainty exists in the map, not in the territory. In the real world, the coin has either come up heads, or come up tails. Any talk of 'probability' must refer to the information that I have about the coin - my state of partial ignorance and partial knowledge - not just the coin itself. Furthermore, I have all sorts of theorems showing that if I don't treat my partial knowledge a certain way, I'll make stupid bets. If I've got to plan, I'll plan for a 50/50 state of uncertainty, where I don't weigh outcomes conditional on heads any more heavily in my mind than outcomes conditional on tails. You can call that number whatever you like, but it has to obey the probability laws on pain of stupidity. So I don't have the slightest hesitation about calling my outcome-weighting a probability."

That's all we're talking about here. This is exactly like the biased coin where you don't know what the bias is. All we know is that our hypothesis is either true or false. If that's all we know, there's no probability other than 50% that we can sensibly assign. (Maybe using fancy words like "maximum entropy" will help.)

I fully acknowledge that it's a rare situation when that's all we know. Usually, if we know enough to be able to state the hypothesis, we already have enough information to drive the probability away from 50%. I grant this. But 50% is still where the probability gets driven away from.

Denying this is tantamount to denying the existence of the number 0.