On March 18, 1980, I was in the U. S. Air Force, stationed near Fairbanks, Alaska. At 5 minutes before midnight, a colleague I barely knew said, "This may be a strange question, but when is your birthday?"
At first blush, that isn't a strange question, so it may seem strange that he thought it was strange.
But as it turns out, it was a strange question after all. My birthday is March 19. At any other time, "when is your birthday" would be just a normal old question. But asking it five minutes before my birthday makes it strange. And prefacing it with "this may be a strange question…" makes it stranger still.