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.