Osmium is rare mainly because of its high atomic mass, and almost all atoms of similar mass are also rare. If it's rarer than the others, it's just an accident of the special nuclear reaction needed to make one type of atom or the other.

These elements are rare in the universe because they rely on rare events to produce them, neutron star collisions, presumably. Of the heavy elements produced by supernovae, osmium is one of the most difficult; it is extremely heavy, hard and dense compared to almost anything that can be created.
Although it is rarely made, it is always there. 65 million years ago, an asteroid containing iridium and osmium hit Earth. Almost all osmium on Earth is in the sedimentary layer next to iridium.
Some elements are rarer than others because the nuclear reactions that produce heavy atoms produce more atoms than others, but for no particular reason any given element is rarer than other atoms of the same atomic mass; although generally speaking, the higher the atomic mass, the rarer the atom.