Probably that’s why logistic function is used to model the probability of a binary event (derived from utility point of view)

Also an intuitive post:

The shape of logistic function looks like the CDF of normal distribution.

As pointed out by Poole et al, the error term of the utility function may follow logit, Weibull, or normal distribution.

We may get prob = logis(xa+b) if error ~ logit distribution.