# What is the link between the logit and the probability of a binary event?

Reading about logistic regression model, I wondered about the link existing between the logit (or $log\frac{p}{(1-p)}$) and the probability of an event defined as binary by assumption and modeled by using the logistic regression model.

I know that transformation has a numerical result that is constrained to the interval $[0, 1]$, and, consequentially, can be directly thought as a probability cause of the latter reason, but, I wonder if it does exist a mathematical explanation to this.

Can someone answer to the question by providing a mathematical proof or reference about?