Using the phrase "draw the short straw" is a little confusing here, because there are 0-n short straws in this scenario. He is describing the probability that t

Using the phrase "draw the short straw" is a little confusing here, because there are 0-n short straws in this scenario. He is describing the probability that there is exactly one short straw (which isn't just 1/n+1 because the straws are not all "present" at once... it's just not a perfect analogy).