Calibration curve motivation

I struggle to understand the mathematical motivation for the binary classification model calibration curve. Why do we assume that the predicted probabilities should be consistent with the proportion of 1's in the probability bin (# of 1's in the bin)/(total # of samples in the bin) ? It's obvious for Decision Tree where the (# of 1's in the bin)/(total # of samples in the bin) ratio is explicitly the model output, but how is this related to the other models? How to show that this ratio and predicted probabilities should be equal?