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An event that only happens once can have a probability (before it happens): this probability represents the uncertainty present in your model of why that event may happen. It's really a property of your model of reality, not a property of the event itself.
Of course, if the event has never happened before, that implies that your model of how it happens has never been validated in practice. You can model the uncertainty present in what you know you don't know, but you'll miss what you don't know you don't know.
But that doesn't mean your model is worthless. Surely we all have the experience of writing a large piece of code and having it work on first try.
Due to nuclear tests being banned, new designs of nuclear warheads are being developed entirely via simulations -- which works (probably?) because our model of physics is pretty reliable.
Bayesian vs Frequentist.
Sharp thoughts. 
It was an interesting question posed by the Bayesian models predicting the US election. The general understanding of statistical predictions in the media and general public was laid bare, when they said that the models were wrong because the election was closer than predicted.
If you have a 99% likelihood that A wins the election, but B squeaks it in the end, does it mean your model is wrong? Surely it implies the outcome of the election was statistically very unlikely, but the model isn’t wrong. If it had said 0% chance for B, then it’s wrong.
if you consider the time dimension... does every event only happens once?
Some would say that this is the only kind of probability. If your model knew enough about a fair coin and how it would be flipped, the probability wouldn't be 50/50
How about the infamous quantum cat that is a linear combination of dead and alive?
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