The precise bounds for the estimate in the absence of monotonicity are as follows:

University of Michigan - Ann Arbor

While having a monotonic function/probability allows for precise computations, the absence of monotonicity does not hinder the calculations of estimates. Instead of a precise value, we then arrive at a tight bound for the estimate.

Effect of Monotonicity

Cinelli, Carlos, and Judea Pearl. “Generalizing Experimental Results by Leveraging Knowledge of Mechanisms.” Technical Report - UCLA, 10 Dec. 2019.

https://ftp.cs.ucla.edu/pub/stat_ser/r492.pdf

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