I\'ve read about neural network a little while ago and I understand how an ANN (especially a multilayer perceptron that learns via backpropagation) can learn to classify an
I can remember I saw an example of Neural network trained with back propagation to approximate the probability of an outcome in the book Introduction to the theory of neural computation (hertz krogh palmer). I think the key to the example was a special learning rule so that you didn't have to convert the output of a unit to probability, but instead you got automatically the probability as output.
If you have the opportunity, try to check that book.
(by the way, "boltzman machines", although less famous, are neural networks designed specifically to learn probability distributions, you may want to check them as well)