Help with an algorithm

Say I have many conditions (C1...n), and one event E. I know the basic probability of both E and C1..n occurring. I'm not too good with this stuff... I need something like

f(C1...n) = P(E)

In other words, how to look at each condition together, as a group, to better predict the event E. There are many thousands of conditions, so generating a power set of all conditions at every occurrence of E and looking for the most occurrences of a particular set is out... it's too computationally intensive.

A little more detail...

C1 may be present when E occurs 50% of the time.
C2 may be present when E occurs 25% of the time.
And do on...

What combination of C1..n most accurately predicts E. Any thoughts?