Meeting new nations: What determines the first contact diplomacy?

Question

When we meet another nation for the first time there appear to be three scenarios.

1. We say "It is an honor to meet you" then they will invite us to reveal their nearest city.

2. We can invite them to "sample our hospitality".

3. A variant of (1), i.e. "It is an honor to meet you" then they will offer to exchange information on capitals, presumably revealing the cities for both sides.

I was wondering what is the cause for each of these three scenarios to happen? I have three hypotheses:

a) it is completely random (my preferred guess so far).
b) it is dependent on whose turn it is, whether it is mine or the AI.
c) it is dependent on the distance to my or their capital/ nearest city.

Edit:

Thanks for Dallium's answer. I think he got it right. But please take note of the following screenshot. In this situation it played out as scenario 1, that is we said "honor to meet you" and Ghandi was like "please visit my nearby city". It was Ghandi's turn, though, and to me this looks more like we were meeting in the middle. We are also closer to Japan than to India.

Answer 1

It's determined by who's unit finds what where.

If your unit finds their city, you'll get case 1.

If their unit finds your city, you'll get case 2.

If your unit finds their unit and both of you are sufficiently far (which (anecdotally) can be anywhere from halfway across the map to 1 hex outside of friendly territory) from your own territories, you get case 3.