Everything in here is a spoiler so I added spoiler tags
The entire audience has access to the information that Spock has spoken to Prime Spock and as such would know what Khan did not.
Prime Spock reveals that Khan was the most dangerous, most ruthless and most brilliant opponent he and his Enterprise ever faced and that they won only at great cost. Without this interaction, it is unlikely Spock could have won, because as he so fond of saying "Vulcans never lie."
Khan, being arrogant, would never consider a Vulcan capable of breaking his word. He never considered that Spock, being half Vulcan and having such a capable teacher as James T. Kirk, would ever do anything that would amount to such an unpredictable lapse of behavior.
Every interaction Khan has made with the Federation since his attacks had gone according to plan. He never considered he might find a match in intellect and in Spock's rage, an opponent capable of being physically his equal. This is Khan's failing, an inevitable over-estimation of his ability with an undervaluing of anyone else's.