There's no need to speculate. This has been documented several times, but only in captivity since they are from different continents.

The King Cobra almost always eats the mamba if they are enclosed together. Its scientific name is Ophiophagus hanna, meaning “snake eater “. That is exactly what a King Cobra is. The vast majority of its diet is composed of other snakes, including venomous ones. The King has a natural immunity to the venom of other snakes, like ”real“ cobras (i.e., genus Naja), that tends to be primarily neurotoxic. Although, mambas and king cobras don't share the same habitat, it's not unreasonable to assume that the King would have a tolerance, if not an outright immunity, to the mamba’s neurotoxic venom as well.

Even if the King Cobra has not developed an immunity to the mamba venom since they do live in different habitats. It is a much more powerful and intelligent snake. The King Cobra is an adept hunter, skillful at delivering the coup de grâce by grabbing its victim behind the head, thereby generally avoiding getting bitten.