William Feller: An introduction to Probability Theory and Its Applications Volumes 1 and 2 - Volume 1 is considered the "classic" in most math undergrad courses, Volume 2 is for masters level students.
Billingsley Probability and Measure - For more advanced probability you need to know measure theory, this is a book dedicated to that.
Karlin + Taylor - First (and Second) Course in Stochastic Processes - If you are interested in learning Ito calculus/stochastics those 2 books are pretty good.
These books have some overlap between themselves but are pretty complementary overall. I would say Feller Volume 1 up to Chapter 11 is decent for non-math people, beyond that you need to be serious about learning.
Didn't put any statistics books as that's a whole different topic.