I think 'chaotic' is a better descriptor than 'probabilistic'. It certainly follows deterministic rules, unless randomness is deliberately injected. But the interaction of the rules and the context the operate in is so convoluted that you can't trace an exact causal relationship between the input and output.

It's chaotic in general. The randomness makes it chaotic and nondeterministic. Chaotic systems aren't that bad to work with as long as they are deterministic. Chaotic + nondeterministic is like building on quicksand.