Some books are a help in understanding things because
they put them differently : a hint when trying to understand
is to follow the historical
evolution of an idea , although this can be quite time-consuming it
does give a real feel of how the ideas came to be,
and the examples are much the same as the ones
given during the courses.(dice, cards, urns, etc )
An easy to read history of some ideas, and the people who thought about them :
King, Amy C. Read, Cecil B. ,
PATHWAYS TO PROBABILITY; HISTORY OF THE MATHEMATICS OF CERTAINTY AND
New York, Holt, Rinehart and Winston 
An interesting recent book with applications in the sciences :
Ruelle, David. CHANCE AND CHAOS
Princeton, N.J. : Princeton University Press, 1991.
Some other introductions to probability that use other words to explain the same things that are done in class :
A PRIMER IN PROBABILITY
New York : M. Dekker, 1979.
DeGroot Morris H. PROBABILITY and STATISTICS
2nd ed. Reading, Mass. : Addison-Wesley Pub. Co., c1986.
A concentrate of the course :
Thorp, Edward O. ELEMENTARY PROBABILITY
Huntington, N.Y., R. E. Krieger Pub., 1966.
A classic on probability - for those who want to go on :
Feller, William. AN INTRODUCTION TO PROBABILITY THEORY AND ITS APPLICATIONS. 3d ed. (New York : Wiley)
QA273.F3712 Two very serious histories of probability :
Hald, Anders. A HISTORY OF PROBABILITY AND STATISTICS AND THEIR APPLICATIONS BEFORE 1750 (New York : Wiley, c1990)
A HISTORY OF THE MATHEMATICAL THEORY OF PROBABILITY; FROM THE TIME OF
PASCAL TO THAT OF LAPLACE.
Chelsea Pub. Co., 1965.