Suggest good sites/books on probability

That book is also good

The main text for 'analysis' is just: Walter Rudin, 'Principles of Mathematical Analysis', McGraw-Hill, New York.

I strongly recommend Elements of Statistical Learning. The text is eye-opening.

Probability Theory: The Logic of Science by E. T. Jaynes

Walter Rudin, 'Real and Complex Analysis', ISBN 07-054232-5, McGraw-Hill, New York.

Sufficient is I. N. Herstein, 'Topics in Algebra', Blaisdell, New York, 1964.

Fooled by randomness would be much better if you want to learn something about probability via a popular author like Taleb, IMO

I would suggest A First Course in Probability, 8th Edition by Sheldon Ross

you can also get the book 'A First Course in Probability' by Sheldon Ross.

Paul R. Halmos, 'Finite-Dimensional Vector Spaces, Second Edition', D. Van Nostrand Company, Inc., Princeton, New Jersey, 1958.

Introduction to probability, D. P. Bertsekas and J. N. Tsitsiklis, Athena Scientific , 2002. ISBN 1-886529-40-X. This is an excellent book for further reading and understanding some of the material.

Jacques Neveu, 'Mathematical Foundations of the Calculus of Probability', Holden-Day, San Francisco, 1965.

H. L. Royden, 'Real Analysis: Second Edition', Macmillan, New York.