If you're female it looks like the oldest living person title is typically held for around a year[1]. Lets say that means 120 currently living people can hold the title, that gives you a 1 in 29 million[2] chance. Which feels far more likely than I would have intuitively guessed.

[1] https://en.wikipedia.org/wiki/Oldest_people#Chronological_li... [2] Or half the odds of a given ticket winning the lottery