Is there a statistician in the house?

How likely is this?

 

So on Monday I fly from NY to Chicago for a conference.  I get on the plane, and eventually a guy climbs over me and into the window seat, and starts up a lively conversation about my incredibly dull reading material (the BABOK--because I'm a party animal).  Turns out he's on his way to the same conference.

 

So far, that doesn't even qualify as a coincidence.  There is a limited number of flights from NY to Chicago, and the conference started late Monday, which encouraged people to fly out during the day on Monday, and this was the cheapest flight.  NY is a large metropolitan area with probably dozens of companies sending people to the conference.  I'd be surprised if we were the only two people on the plane headed to the same place.

 

We struck up a little acquaintanceship which lasted until we got to the hotel and the conference, at which point we got routed into different tracks because our professional interests in the conference topics were different.  We turned up in the same session only once, and didn't really see each other at all while the thing was going on.

 

The conference ends, and I go back to O'Hare and check in for my flight.  I get some lunch.  I sit down to wait.  Just as the flight is about to come in, the dude shows up and says, "I figured you'd be on this flight."  Again, we were flying the same carrier, so this doesn't really qualify as a coincidence.  Then he says, "I'm in seat 14A.  If you're in 14B, I'm going to be seriously weirded out."  And indeed, I was in seat 14B.  OK, now it's odd, right?

 

Or maybe not.  How likely is that?  The plane wasn't huge--only 25 rows of 6 seats, so on the small side of the commercial, non puddle-jumper plane size.  But seriously?  The same two completely unrelated passengers sitting together twice in a row?  I'm interested in how likely that is, and whether it might have to do with some airline convention that I'm not aware of.  (Like, does it matter if our last names start with the same letter or if we reserve our flights at the same time or check in at the same time or....I don't really know what else.)