Pick up Jaynes' Probability Theory and turn to the section on decibels of evidence, an even more convenient measure. Or for a summary see Eliezer's 0 And 1 Are Not Probabilities in the sequences.

When you work in log odds, the distance between any two degrees of uncertainty equals the amount of evidence you would need to go from one to the other. That is, the log odds gives us a natural measure of spacing among degrees of confidence.