How to get the posterior probability of the outcome?

[KatatoniaSh]

I have trained a model and used budget optimizer and I got the expected outcome. However, I want to do inference and determine the probability that the outcome will exceed a threshold (maybe the non-optimized excpected outcome). I am wondering how I can get the posterior dist. of optimized outcome (or even non-optimized outcome).
As a another question, how is it possible to draw the posterior dist of outcome for both non-optmized and optimized outcome?

[KatatoniaSh]

I am wondering if it is possible to have those?