Ternary logic is a super simple model; where true AND unknown equals unknown, and true OR unknown equals true. This deals with uncertainty and ambiguity, just not the probability; notionally you could say everything is 50-50.
Same thing if you have e.g. text-to-speech which returns "the b??? dog" rather than "the (0.8:black, 0.1:blue, 0.1:boy) dog" - no probabilities. Of course, maybe later in the processing you add probabilities back in.
Then there's fuzzy logic, which uses scores that are typically numbers, but those don't express actual probabilities, but more like vibes. They don't necessarily add up to 1, for instance, and you don't apply Bayes' formula to them, or even multiply them, you can use addition too - yolo.
Edit: and also of course backtracking, beam search, that sort of stuff - needn't use probabilities, just heuristics.
Anyway, the probabilistic model doesn't exist. Simple probabilistic models work quite badly on speech recognition (word classification, etc.). A lot of structure needs to be added before they start performing.
A probabilistic model is the most complicated model. It doesn't even attempt to model the problem, it just looks at the results of an enormous number of tries with different inputs, goes through them all, finds the most similar cases to the current input, and blends them together in a way that carefully avoids any self-contradictory or absurd result.
We see this plainly with LLMs. You train an LLM on a thousand times the (high-level, pre-digested) input that the average human has gotten, and the average human thinks it's a hallucinating moron. It doesn't start to converge on something that passes the smell test to you average human idiot until it has been trained on a million times the input the average human has gotten.
It's not doing what a human does, it's guessing what a human (or any system) might do when confronted with X input. They're not even similar activities, even if they have identical output in the limit. It's like confusing gravity for equations about gravity. Being able to make perfect predictions about the positions of moving, nearby frictionless spherical things in a vacuum at time t doesn't tell us a thing about what gravity is. It tells us how it looks. It should, we distilled it by watching things for a very long time.
> Is a probabilistic model not the only model able to deal with uncertainty?
No, all models deal with uncertainty. The entire point of a model is that it is what you know about a system when you don't know its inputs. The variables in a model are uncertainty. The model is dealing with it.
edit: I think you're interpreting "uncertainty" as a numerical probability. A numerical probability is an artifact of the set of data you're calculating it from, not a thing with independent existence. "Uncertainty" is just a thing that you don't know yet.
If you assume that "uncertainty" is a knowable numeric probability that contributes to some calculation, you're begging the question when you say that the only way you can model it is through probabilistic calculations.
For the domain I am working in, a model is considered deterministic if for a set of input it always provide the same output and the input are assumed to be perfectly known. A model become probabilistic, once the input or the model itself are considered as uncertain. As an example: previously weather models always provided singe prediction for tomorrow, for example rain or no rain. But now, such models are probabilistic in the sense that an ensemble of model forecast are made (with slightly different input representing our uncertainties) to provide an estimate of the probabilities. Indeed such probabilistic model is not the simplest, but to most complete and so far the only practical way to handle with uncertainty for system like the weather as far as I am aware of.