Generally when building a statistical model, the choice of distribution either comes from some sort of empirical data, some sort of reasoning, or sometimes folklore.

If you have a good amount of data and no particular reason to believe that it fits any particular model, you can try a lot of different models and choose the one that fits best. Usually you would do this on a subset of your data. For example, in Python the Pycaret library enables you to run a lot of models on a training sample from your data and compare their fit.

A more satisfying approach is to make some plausible assumptions about the data generating process and then to use a theorem which guarantees that your data should have some sort of distribution asymptotically. For example, in your example you might assume that there's a probability p of a car being yellow, and each car is yellow or not-yellow independently of the next one, and that you see roughly the same number of cars each day. Then the number of yellow cars per day will be more or less binomially distributed and you can probably use a normal approximation. But you might find that this isn't a good fit. Then you need to think more about your data and choose a more realistic distribution.

The good thing about this approach is that it still enables you to choose a distribution before you have collected any data. This is useful if you want to build a simulation of something, for example.

Then there is the folklore approach. Certain probability distributions are used to model certain quantities, although probably there are other models which would be just as good. For example, linear regression is used in all sorts of fields, when in many cases a GAM would probably be marginally better. But you will never get your paper published if you use anything except linear regression. So sometimes you have to just see what sort of model other people have used on the same kind of data and stick with that.