The best reference is Jaynes's Probability Theory: The Logic of Science. The first three chapters are online for free and explain the development of probability theory as a logic for plausible reasoning [1]. If you want to get a quick taste, I wrote a short blog post that introduces the theory while working through an interesting coin-toss problem [2].
[1] http://bayes.wustl.edu/etj/prob/book.pdf
[2] http://blog.moertel.com/posts/2010-12-20-more-on-the-evidenc...