This can, at best, only be speculated at. All of the information currently relies on human input and trust. Especially with how emotional gamers are, you cannot rely on this 100%.
Is there a mechanic that makes your next legendaries hard to get? Probably. It could also just be a catch up mechanic for people that don't have 1 yet. We can't see the data.
If there is a mechanic in place to make the next ones harder, how much? Impossible to tell with any reliable certainty. The data is just too dirty.
All of that said, your 3rd legendary is going to be easier to farm than it is going to be to relevel to 110, get all of the same gear, and roll the dice on another legendary.