There is a simple closed form solution, but I wanted to do a brute force Monte Carlo simulation. I randomly assigned two spots on the circle for the two ghostbusters (Abe and Betty) and then assigned two spots for the ghosts (Dan and Candace). Then ran multiple simulations and tracked of the streams crossed or not.
The convergence plot below shows how ~1k sims convergence to the solution of 33% chance that they cross streams.
See the Jupyter Notebook.