One of the key benefits of the propositional representation was our ability to represent our knowledge without explicit enumeration of the worlds.  In turns out that we can do the same in the probabilistic framework.  The key idea, introduced by Pearl in the Bayesian network framework, is to use locality of interaction.  This is an assumption which seems to be a fairly good approximation of the world in many cases.

This representation supports many interesting reasoning patterns.  For example, if we observe that the student gets an A, the probability that he is smart goes up.  But if we then find out that the class was easy, it reduces the impact of this evidence, and our probability goes down, although not all the way.