RenBFirst, we wouldn't ever compare "likely" and "likelihood" directly. The former is an adjective and the latter is a noun, so they are used in different constructions. If you are
likely to do something, there is a strong
likelihood that you will do it. In the reference question, the one answer with "likely" just doesn't use a sensible construction. We can't say "the greater was something [adjective]." In general, we'd say that something is MORE LIKELY or that it's LIKELIHOOD was GREATER.
As for OF vs. THAT, as with many idioms, there isn't one answer. It depends on what you are saying. LIKELIHOOD OF would be followed by a noun. "There is a high likelihood
of rain." LIKELIHOOD THAT would be followed by a clause. "There is a strong likelihood
that I will stay home tonight."