To actually do any measure of probability experimentally would require an infinite number of trials, but we can do many trials, and get a reasonably good idea of what it is likely to be.
Certain assumptions (like assuming the probability of tossing heads with a coin is 0.5) allow very powerful deductions to be made.
Significantly, probability is subjective, not objective. Different people have different opinions about what a particular probability is, and it can never be comprehensively tested.
Two people might make an estimate of the probability of a horse race, and might even make bets with each other based on those probabilities. One of them will win, but that does not prove he was right. A punter who consistently makes good bets, and makes a lot of money from betting on horse races is probably a better judge of those probabilities than a punter who has lost a lot of money, but that does not make his measure of probability correct in any instance - it is merely strongly suggestive that his measure of probabilities are better in general.
See