What is required of one who thought madhy (pre-seminal fluid) had exited him but was not certain, then performed ablution and prayed, and did not realize this until after his prayer?

As long as a person is not certain about the emission of prostatic fluid (madhiy), their prayer is valid, because the default is that it has not been emitted, and certainty is not removed by doubt. Predominant conjecture here is considered doubt by jurists. However, if one is certain about the emission of prostatic fluid and forgets to purify from it, then prays, their ruling is like one who prayed with a known impurity that they forgot or were initially unaware of. The majority of scholars hold that their prayer is valid and they are not required to repeat it.