There is a huge literature on interpreting probability and this is even larger if you just look at examples of how people use it. A really good place to start is to follow the references mentioned in Hájek's encyclopedia article. A heavily overlapping list including lots of book chapters (among other things) can be found on Branden Fitelson's Probability and Induction course website: Syllabus

Frequency accounts of probability:

- von Mises, Probability, Statistics, and Truth
- von Mises, On the Foundations of Probability and Statistics
- Jeffrey, Mises Redux (in Probability and the Art of Judgment)
- van Fraassen, Relative Frequencies
- Hájek, "Mises Redux” — Redux: Fifteen Arguments Against Finite Frequentism
- Hájek, Fifteen Arguments against Hypothetical Frequentism
- Hájek, The Reference Class Problem is Your Problem Too

Propensity accounts: