How to find the regression model log likelihood of data $(x, z, b)$ where $b$ indicates whether $y > z?$

I have a dataset where I don't have the exact output labels $$y$$ but what I have is if $$y$$ is larger or smaller than another value $$z.$$ There is another binary parameter $$b$$ that decides if y is larger or smaller than $$z.$$ If $$b=0,~ y$$ is smaller than $$z$$ and if $$b=1,~ y$$ is larger than $$z.$$ I want to develop a regression model for this. more specifically I want to find the log-likelihood for the observed data which is a triple of $$(x,z,b).$$ How do I go about solving this problem?