Conditional markets ask 'if X happens, does Y follow?' (e.g. 'if Newsom is the nominee, does he win?'). They give you a clean conditional probability that you can compare against the plain, unconditional markets using basic probability math: the chance of being nominee, times the chance of winning given the nomination, should equal the chance of winning outright. When those pieces don't multiply out correctly, you trade the legs against each other. The edge is the inconsistency between the conditional price and its parent markets.
Markets on Polymarket where conditional-market trading is the natural play: