I don't know about "should", but my distribution would be something like

red=0.24 blue=0.2 green=0.09 yellow=0.08 brown=0.04 orange=0.03 violet=0.02 white=0.08 black=0.08 grey=0.02 other=0.12

Omega knows everything about human psychology and phrases it's questions in a way designed to be understandable to humans, so I'm assigning pretty much the same probabilities as if a human was asking. If it was clear that white black and grey are considered colors their probability would be higher.