You may want to have a look here...
Amazon.com: calculus based probability: Books
You may want to have a look here...
Amazon.com: calculus based probability: Books
Can you be more specific about your needs, particularly about the level?
As you say that are many different books.
As a general text I prefer, Probability by Jim Pitman. It is just a good all around college level text.
If you want more statistics then try: Mathematical Statistics by Larsen and Marx. This has good section on counting.
A higher level text is Probability: Theory and Examples by Rick Durrett. It is excellent on: Random Walks, Martingales, Markov Chains, Ergodic Theorems.
The text by D.L. Minh, Applied Probability Models is packed with high level applications and examples.
You may be looking of a graduate level text?
My College uses the book, Probability: A First Course.
I ordered it, but never read it because I never liked probability. I just have it because I am taking Mathematical Probability next semester in hopes of actually liking it.
Note, though it is a "first course" it is a first course for mathematically serious students. So it is an adnvanced book.
And it has bad reviews because most people who ordered it thought it would be an easy book (non-mathemations learn probability too) based on its name.
I heard that from my classmates in class. We were talking about integration and I asked the professor if he can explain what Lebesque integration is about. As he was explaining some of the students (which are also in the probability class) spoke up and said that their professor uses that term a lot, though they never do it. I remember them saying that in distributions some things can be simplified with measure theory.
But that probability class that you were talking about is probably a graduate course.
Technicaly I think not, but only on a technicality, Part 3, at Cambridge is
nominaly an undergraduate course (though I know at least one person from
another university who was given a master course grant to do Part 3 as a
one year course after getting a BSc in Maths)
RonL