The quickest way to see why is to imagine a slightly different way of drawing straws. Instead of drawing straws, draw cards where all but one are black (for example). The fact that when drawing straws we pull one at a time and generally stop halfway through (whenever the short straws appears) makes it fell like the situation is different, but it’s not. The second person has N-1 straws to choose from, so you might expect that their chance of drawing the short straw is . So, all in all, the probability of the Jth person drawing the short straw is .