It's not a stupid question, but it's not the sort of question that has an answer.
The big exciting thing that's going on with complex numbers and probability is Schramm Lowener Evolution.
There was a slightly obscure idea in complex analysis called the Lowener differential equation. Essentially given any function on the real numbers I can associate a path in the complex plane that never crosses itself. It was clever, but never really took off as an idea.
Then a guy called Oded Schramm came along and solved the Lowener equation for a Brownian motion (A very random function) instead of a deterministic function.
The solutions of these are random paths in the complex plane that never cross themselves. It turns out they are also conformally invariant. (If I apply a differentiable complex function to the solution of the Lowener equation the probability distribution of the solution doesn't change.)
This area has seen a massive explosion of research in the last ten years. And there's an attempt to use these ideas to try and unite Quantum mechanics with gravity.
That's the only thing I can think of where there's a real union of complex analysis and probability theory.
It's definitely not something I'm an expert on, and it's a seriously hard subject. (Two fields medals in the last ten years.) But it's probably worth your time having a look at what's going on in this area.