I am looking for a book for self-study of rigorous probability theory. I would like a book which is at a completly introductory level, but which is rigorously written. Especially not welcome are books like Introduction to Probability by Sheldon Ross ( which is a great book in its own right ).
The book should have as little assumptions as previous knowledge as possible.
Analog to the book I am looking for is something like Spivaks Calculus or Apostols Calculus but for probability theory.
I am really really stuck,since I suck at learning non-rigorous mathematics,and I always happen to land into some corner case when I try to apply it.
Thanks in advance