The incident with the ex is believable. It's even the starting point of their lives crossing each other's. I have no qualms about it.
The present "problem" in the story, is that No-rae feels something was not quite the same when she got skinship with Seol-a than when she got skinship with the other guy. So she "retreats" because she's trying to sort out her feelings. That much I understood. So we watch them grow a little apart because of this. That's the current state of affairs. I'm okay with it.
Now, we all know where it's heading : the author has to find a way for them to get close again, with a little bit of drama.
But over-hearing a conversation at the vending machine about precisely the person that's on your mind and what she's doing right now and with who, completely by sheer dumb luck is bit too much for me. It advances the story, okay, but it seems artificial to me.
And I'd rather take the wikipedia definition : a seemingly unsolvable problem is suddenly and abruptly resolved by the contrived and unexpected intervention of some new event, character, ability or object. Depending on how it is done, it can be intended to move the story forward when the writer has "painted himself into a corner" and sees no other way out, to surprise the audience, to bring the tale to a happy ending, or as a comedic device.
It's not the event in itself I criticize. It's the way No-rae is involved in that event.
Ssamba didn't have to do it that way, in my opinion.
It really is a minor point, but it ticked me off
But, who am I anyway ? The author does what she wants.