I recommend "Introduction to Probability" by Joseph K Blitzstein and Jessica Hwang.
This book is tough. Really tough. However, you are really going to do "deliberate practice" while having a go on the assignments.
It bothers me that the author does not provide the answer to most of the questions. This is specially bad in this field of Mathematics (Probability). As an example, in calculus you can always plot the curve, the derivative and see if the result makes sense, in probability theory it is hard to have a simple and safe sanity check.
You can watch all classes from Harvard here for free: https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB...
If you want, there is also a MOOC in EdX with the same material: https://www.edx.org/course/introduction-to-probability-0
Sheldon Ross' book is also a good one. It was mentioned here. I specially like the section on theoritical problems, only with exercises on proofs. Every chapter has one. However, Joe Blitzstein problems are more challenging and will train you more on intuition.