Books similar to Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller I find the book Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller.
I would like to solve more probability problems whose levels are similar to book above. 
Does anyone have good suggestions?

The closest to Mosteller's book is probably Yaglom's Challenging Mathematical Problems With Elementary Solutions: Combinatorial Analysis and Probability Theory. It was published around the same time, the problems have a similar flavor, and it doesn't require any knowledge of measure theory.
You may also be interested in Patrick's Intermediate Counting and Probability, as well as in the chapter "Combinatorics and Probability" of Andreescu's Putnam and Beyond.
