I think someone earlier said something about not quite getting the joke, and I confess I wasn't so clear on it either until he explained.
For his generation, Pearl Bailey was a huge name that everyone knew. On the MEF forum, he said
"Yes, that is my ALL TIME favorite joke. But alas, the Pearl Bailey reference is lost on today's youth. She was a huge star in her day."
He also went on to say (in 2010) "Holy crap, I just thought about it. I have been telling that joke for over 50 years now."