Those questions underpin big chunks of philosophy.
Assigning a probability to a one-off event is enumerating all the ways it could happen, all the ways it could not happen and assigning a probability to each of those ways. Obviously there is a lot of guesswork; but if you need to make a decision based on the future that approach gives you a much better chance of making a good decision. In practice an event will be made up of components that are more predictable than the whole, and some real uncertainties. There is a lot to be gained by thinking hard about the situation, and assigning a probability will do that.
Silly example - how do I estimate my risk of falling climbing up a set of stairs that I've never climbed before?
* Baseline risk of tripping - I have a lifetime of data.
* Increase of risk being on a staircase - I have an area I want to put my foot on (a specific step) that is about 1/3 of the area that my foot usually falls in, so that increases the risk by an amount that can be reasonably estimated.
* I will watch my foot - maybe an order of magnitude improvement in precision.
This is enough to let me estimate the risk of carrying a bulky object (that obscures my view of my feet) up a staircase. I've isolated the uncertainty (how much does visual observation change the odds) from the certainties (areas, background rate).
Now I can take that to several experts who will identify new mechanisms and tighten up my estimations on how big a deal the components are. In this way - even though the final % I come to would still be a bit arbitrary - it is starting to become a summary of what a large number of people think about the inputs to the problem and their relative magnitudes. Being able to communicate all that thinking with a single number is a miracle in its own way.