I'm reading the textbook "Introduction to Econometrics" by Stock and Watson. Chapter 11 discusses regression with a binary response and it teaches the logit/probit models mostly. These seem to make sense when the plots show an S shaped relationship between X and Y, but what if I'm working with a dataset where the model calculates a probability in the shape of a "hill".

For example what if my continuous predictor X ranges from 0-100 and my response Y is only equal to 1 for X's at values of 30-70 but gets more concentrated at X's around 50. So lets say around X=50 we could have a 40% probability of Y=1, and then at X=40, X=60 we'd have 25% probability of Y=1 until the probability of Y=1 dissipates around 30-70. I cant find any models that model such a relationship through google - Are there any models that are more appropriate than logit/probit for this type of relationship?