[Keysh]

That means massive black holes have a much lower density that small black holes. So they are more likely to form than small black holes.

No, it doesn't, because you're ignoring all the physics required to get the mass into a small enough region so that it will collapse to form a black hole. The only way to make that happen that we know works is to form massive stars, where a fraction of the star's mass, in the center of the star, will eventually form a black hole. But the largest stars we know of have masses of ~ 200 times the Sun, and so can't form black holes more than a fraction of that.

If you imagine a more massive gas cloud collapsing under its own gravity, it will fragment into subclumps before getting very dense; these subclumps will themselves fragment or go on to form stars directly, but with an upper limit of, say, ~ 200 solar masses.

(It's possible that if you start with a cloud of pristine gas in the early universe -- nothing but hydrogen and helium -- that it might collapse to form a single supermassive star, or even a black hole directly. That might give you something like a 1000-solar-mass black hole. But that's still fairly speculative, and requires unusual conditions that don't exist generally.)