Think of it as a sealed box containing one marble. You know that the colour is black or red. And you know nothing else.
Then what is the probability of it being red?
The probability is unknown.
The reason we sometimes think of these things as being 50/50 is that usually this kind of sentence construct is describing something that is implicitly 50/50. For example, if you don't know which way the nearest toilet is and you need to decide whether to go left or right, you will have a 50% chance of going the right direction. Why? Because there is an implicit assumption that toilets are evenly distributed throughout the building; that there is no bias in the building towards building a toilet towards the building's left or its right. If you know nothing else, then you assume this. And it's a pretty reasonable assumption, that nobody would call you on, because all of your experience in real life tells you that buildings have no bias either way: some buildings have toilets to the left, others to the right.
More mathematically, assume there is only 1 toilet. You don't know where the toilet is. You also don't know where you are. For all intents and purposes, the toilet is randomly distributed on a x-y plane, with you at the origin. Key phrase:
randomly distributed. When a thing is randomly distributed on a plane, there is an equal likelihood that it is to the left or to the right of the origin -- or at least, that is the implicit assumption that you're making. And, again, this assumption seems valid when we compare it to our experiences: toilets don't appear to have any bias towards appearing to our left than to our right, or vice versa.
So when you talk about red or black balls having a 50% chance of showing up, you're making an implicit assumption that those balls are evenly distributed. And, at a push, I would agree that the balls are evenly distributed -- because when people pose that sort of question to you, they usually mean to imply that they are evenly distributed. My experience with picking either black or red backs this up: Black and Red show up in equal numbers on roulette tables, and there are an equal number of black and red cards in a standard deck of playing cards. But my experience also tells me that there might be more red than black balls: what if the person posing this question took balls from a snooker table, then picked one at random? 9 reds or whatever vs 1 black. Not 50/50 now is it. But usually, when people ask me to pick a coloured ball out of a bag, or guess which coloured ball is in a bag, they mean to imply that there is an equal probability of me guessing the right ball. And indeed, in asking me to pick a colour, red or black, they are usually making the assumption that there is no human bias or predilection in favour of red over black, or vice versa. So there is an implicit mutual agreement here, one that is unwritten, but one that is backed up by countless social interactions and experiences with picking either a Red and a Black.
Another way of thinking about it is this: you are making an assumption about how the red or black ball got there. If you assume that it was picked randomly, then you have to make an assumption about what it was picked randomly from. Is it snooker balls? Or is it a bag that contained an equal number of balls? You can again use your experience as a guide here. If you assume it was picked deliberately, then you have to make an assumption about the person picking. Does this individual have a bias? What is the probability that this individual has a bias? Again, experience can be the judge: maybe if it was a ball that smelt like crap vs a ball that felt like boobs, then more people would pick the boob ball than the crap ball. But with red or black, your experience tells you that people don't really have a preference either way. Or maybe they do -- maybe
you do, but you don't know it. Well, again, we're back to the toilet distributed on a plane -- except there are two toilets. What if the toilets have a bias to the left? Well, the first toilet might land at some co-ordinate, but the 2nd toilet still has an equal probability of landing to the left as to the right of the first toilet.
Again, though, the point is you use your experience to make some assumptions about the problem. You never have zero information: you have some biases about the problem, and you use those biases to come up with a probability. In your case, you've decided that a person asking that question would probably mean to imply that it's a 50/50 deal. I suspect that most people would think similarly. But the point is, what we're doing is building some assumptions in order to calculate a probability, and those assumptions come from our real life experiences and interactions with similar problems.
There is no such experience when we talk about God, however. We don't have anything to back up the idea that there is an equal probability that God exists. In fact, we have a lot of experience to suggest that God doesn't exist -- we've never seen him or heard him or anything. So you can't use this same implicit assumption of randomly distributed toilets or randomly selected balls from a snooker table or whatever. There's nothing that you can use, no experience that can guide you; or, worse, the only experiences you have suggest that God doesn't exist.
So no, 50/50 isn't in any way the default probability you assign to unknown outcomes. There's always some assumption you're making, if you assign a 50/50.