I agree that knowledge of computer science doesn't transfer directly to climate science. However, there's a lot about computer science that may help understand how climate models yield probabilistic outcomes (Monte Carlo, anyone?).
On the subject, be a little careful equating probabilistic models and statistical models. At least in my experience, "statistical models" generally describes statistical fits to past data. Think of a polynomial whose parameters are chosen by least-squares fit to previous observations. These fits can be used to interpolate or extrapolate (to the future, or to different combinations of inputs). However, they don't encode any domain knowledge, and they can be extremely brittle when pushed outside the regimes from which they were derived.
Most climate models, on the other hand, are deterministic, physics-based models. Some of the sub-models may have statistical fits in them, but the modeling is largely driven by some conceptual framework of how the physics drive the dynamic system (e.g., expressing conservation of mass and energy, and how spatial differences drive transport).
Those deterministic climate models can be driven probabilistically-- meaning the uncertain inputs and parameters can be sampled from distributions of likely values. Aggregating all the results gives a probabilistic prediction. A lot of climate reports take this one step further, and aggregate results across multiple models. Most computer scientists will immediately "get" this part, even if they don't understand all the physics represented in the individual packages.