Use distribution probability as a feature in ML model
As a general approach I would say you need to generate new features, that use your prior knowledge. For example, if you have a known size distribution, then for each specific size you can calculate its probability and use it as a new feature.
As I side-note, the geometric distribution of cow sizes seems very surprising to me, I would expect to see some gamma distribution or just normal (if size is measured in cm/inches).