This seems closely related to this classic Functional Pearl: https://web.engr.oregonstate.edu/~erwig/papers/PFP_JFP06.pdf

It’s so cool!

I always start my introductory course on Haskell with a demo of the Monty Hall problem with the probability monad and using rationals to get the exact probability of winning using the two strategies as a fraction.

See also the Haskell library monad-bayes https://monad-bayes.netlify.app/tutorials/ https://www.tweag.io/blog/2019-09-20-monad-bayes-1/