For example, if we had an arbitrary event that could either yield the result a or b, we might naively assign a probability of .5 to each result. After several trials, we can use the results of the trials to adjust our expectations of the probabilities of the event yielding a or b. If the first n trials result in b happening we expect b to happen in the next trial with probability (n+1)/(n+2). My question is, how does this generalize to other such situations? If, let's say, there was another arbitrary event which had 5 possible outcomes, we might naively assign each result a probability of 1/5 prior to any trials. How would we then adjust our expectations as the trial results come in?