He made that leap because they were operating under the assumption that Bran had seen something he shouldn't have and was therefore pushed. Jaime and Cersei both had abstained from going on the hunt with Robert, so there was at least ability if not motive in pushing Bran.

Ned is informed by Cat's sister Lysa, Jon Arrington's wife, that Jon had been murdered. He jumps from that to figuring Jon had also found something he shouldn't have known. He follows the trail and figures out that if Joffrey et al were Robert's kids, they should have had black hair. Sansa made that offhand remark about Joff being a lion, not a stag, that probably got his mind creeping in the Cersei/Jaime direction.