We observe all three categories.
Because the theory that describes it is purely probabilistic, not deterministic.
We have models based on, say, ballistics which describe the paths of projectiles in a deterministic and predictable way.
We have models of weather systems which are deterministic but can only make predictions within certain bounds and with a certain probability.
And we have models of quantum behaviour which are purely probabilistic. There is no "mechanism" or deterministic-but-too-complex description. And there are good theoretical reasons to think that no such description can exist.
All of these are, as you say, based on observation. (They must be; they are all scientific models.)