I sorta think about it as "what's the likelihood of someone winning the lotto twice in a year?" Certainly the probability that any specific person wins twice (assuming here these are independent events...) is so ridiculously small. And yet probability at least 1 person somewhere is that lucky is incredibly high!

Now ask if my neighbor looks like any random person on the street, sure, it's small. But that chance we find two people somewhere that look very similar is incredibly high.