What is the best book to learn probability?

For probability theory as probability theory (rather than normed measure theory ala Kolmogorov) I'm quite partial to Jaynes's Probability Theory: The Logic of Science. It's fantastic at building intuition behind the rules and operations. That said, this has the downside of creating fanatics who think they know all there is to know about probability theory.

A First Course in Probability by Sheldon Ross is good.

If anybody asks for a recommendation for an introductory probability book, then my suggestion would be the book by Henk Tijms, Understanding Probability, second edition, Cambridge University Press, 2007. This book first explains the basic ideas and concepts of probability through the use of motivating real-world examples before presenting the theory in a very clear way. I found a nice feature of the book the fact that simulation is deliberately used to develop probabilistic intuition. The book also discusses more advanced topics you will not easily find in other introductory probability books. The more advanced topics include Kelly betting, random walks, and Brownian motion, Benford's law, and absorbing Markov chains for success runs. Another asset of the book is a great introduction to Bayesian inference.