You may wonder why we cannot simply write P(1) = e - /τ . The reason is that we are not guaranteed that the sum of the probabilities is equal to one yet, and therefore we can only talk of relative probabilities right now. In order to speak of the absolute probability we need to introduce a new concept.
The normalization denominator in equation is something we are going to encounter again and again, so we might as well give it a name. It is called the partition function and is denoted Z. That is: