From a course i am following, the following interpretations of probability:
Objectivist:

• Frequentist, only repeatable experiments have probabilities.(thus very limited)

• Propensity. Everything has an objective chance of it happening intrinsic to that thing. Like a pen has a high propensity of falling, if i let it go. (even if i never do let it go, or only once)

Subjectivist

• Everyone can assign their different probabilities to different events. Usually a additional requirement of rationality is required; this meaning: No one can devise a game in which that person would always lose. (this meaning, that someone can use probability theory to devise a game in which the opponent would always eventually lose)

• Logical interpretation; takes the rational side farther, claiming that based on the same data, there is only one logical result as probabilities. I think this one is too strong, it is known that in infinite cases, the initial probability is arbritrary. (even with the principle of indifference! see below)

The principle of indifference: Given no other information, different cases have the same probability.
Problem thereof: If the set from which is randomly chosen is infinite, there is no transformation-invariant uniform probability. (and many transformations will be reasonable) Should give an example here, but i forgot it

PS took the explanation of probability too far, ah wrote it now so i will post it.