You are right about the problem. Probability theory requires a future event (on the assumption that the outcome is uncertain), because if the event has already happened or not, its probability is 1 or 0. But if the outcome is not known, even if it is in the past, one can calculate a probability for it. One could articulate a probability for a past event, provided one uses the past tense - "the probability was x (at the time in question), so that you can then say the outcome (at a later time) was . Of course, one needs also to ignore the fact that the outcome is known. The question would be something like "If we didn't know what the outcome was, what probability would we assign to it."
The bottom line is that a probability requires a change.
Pascal's wager illustrates the way round this. Pascal proposes we consider the event of our death and our prospects after death. The probability of my going to heaven or hell satisfies the requirement.
But probability requires more than that. It requires a list of possible outcomes. Coin-tossing and similar games satisfy this. Empirical questions are more difficult. The process there is to rely on past experience (statistical evidence) and a "confidence interval", with further complications around infinitely variable outcomes like temperature.
We could ask what the probability is that we will discover that God exists, or that there is no such entity or that we will never discover whether there is such an entity or not. But those would be meaningless, since there's no time limit. So we need to impose one, such as "in the next ten years" or "before I die".
But it is still a one-off event, so there is no alternative to Bayesian probability which works on assigning a level of "credence" to an event. (I think it probably (!) still needs a time limit.)
There is, however, another requirement for probability. Probability can only be assigned to an empirical proposition that might be true or might be false. But I think that God exists is a hinge proposition - roughly an idea that governs the way that evidence is interpreted. If one accepts it, one interprets all the evidence one way. If one does not accept it, one interprets the evidence in another way. One could not assign a probability to it. That's an over-simplification, but I think it works in this case.