The comments on the Althouse post have a lot of smart people trying to figure out the probability and arguing about how unusual it is to deliver 19 boys in a row and if we should be impressed. The point is made repeatedly that every combination of boy/girl deliveries is equally likely, which of course is true. As I was reading through the comments though, it occurred to me that people are getting way too hung up on the quantitative probability here.
The real question is much easier: are there any other combination of 19 deliveries that would have been as interesting to you? Out of 524,288 possibilities, only 19 girls would have been as interesting as 19 boys. For some it would be equally interesting at 18, 17 or 16, some not. It's a little like a lottery ticket coming up 1 2 3 4 5 6 or 4 8 15 16 23 42.
The chances of something interesting happening are directly proportional to how many outcomes you find interesting. That's what I call a qualitative probability, not a quantitative one. It's like that post from thankstextbooks.
*The Althouse post says 14 hours, but the article says 62 hours, not really sure where the discrepancy came from.