The probability that someone is the first is 100%, but the probability that we are the first is (presumably) much lower.

It's like you're meeting a whole bunch of people, and you arrive slightly before the agreed upon time, and there's nobody there. Could be that everyone else is just cutting it close, but you'd expect at least some people to arrive early. It's pretty unlikely that you'd be the first one there. So you start to wonder, are you in the right place? Did you get the date wrong? Did you miss an e-mail?