I am trying to model an optimization problem in which the constraints have the following structure:
$_{min}f(x)$ such that:
$a(x)\geq b$ with probability $p$
In my real model, I have the expressions of $a$ and $b$ and just for making it clear I marked them as $"a"$ and $"b"$.
Now my question is how can I incorporate this probability into my constraints? Thanks
That is called a "chance constraint". The study of optimization problems containing chance constraints is called Chance-Constrained Programming. There is a large body of work going back several decades on formulating and solving such problems. The algorithms to solve such problems depend on further details of the problem.
Here are a couple of accessible introductions to get you started. https://web.stanford.edu/class/ee364a/lectures/chance_constr.pdf
https://optimization.mccormick.northwestern.edu/index.php/Chance-constraint_method