It's not entirely unrelated, the fact that the system is non-deterministic means that it necessarily is probabilistic.
A business can reduce temperature to 0 and choose a specific seed, and it's the correct approach in most cases, but still the answers might change!
On the other hand, it's true that there is some probability that is independent of determinism, for example maybe changing the order of some words might yield different answers, this might be a deterministic machines, but there's millions of ways to frame a question, if the answer depends on trivial details of the question formatting, there's a randomness there. Similar to how there is randomness in who will win a chess match between two equally rated players, despite the game being deterministic.
> the system is non-deterministic means that it necessarily is probabilistic.
This is not correct. Both of the examples I gave where specifically chosen because they use non-determinism without any probabilistic framework associated.
Regex matching using non-deterministic finite automata requires absolutely zero usage of probability. You simply need to keep track of multiple paths and store whether or not any are in valid state at the end of processing the string. The list monad as non-determinism is an even more generic model of non-determinism, that again, requires nothing probabilistic in it's reasoning.
Non-deterministic things do often become probabilistic because typically you have to make a choice of paths, and that choice can have a probabilistic nature. But again, NFA regex matching is a perfect example where no "choice" is needed.
How many paths are there in that regex, say n. If n1 of those paths lead to one result, and n2 of those paths lead to another result, then you can model the probability of the first path being n1/n. There you go probability.
I do agree that there is no designed probability in that example though, but there is emergent probability.