I believe the events are independent in that each time the theoretical monkey hits a key it has a 1/26 chance of being a specific letter. This means that each letter has a 1-(25/26)^36 probability of occuring in a 36-character sequence. If one of the letters is an H it really doesn't effect the chance of an E showing up because if it wasn't an H it would still be something other than E.

Simply put the chance of all three specific letters showing up in a 36-character sequence is (1-(25/26)^36)^3.