Sometimes N=2 is extremely different from N=1. Specifically when we have N=1 and we suspect that it might be unique, or extremely rare to the point that you wouldn't expect to find instances.
Sometimes N=2 is not that different from N=1 though. Specifically when you don't think the situation is necessarily that rare, you just don't have a big population to choose from. That's the situation here.
Astronomers expect to find other Earth-like planets. We suspect rocky planets aren't that rare, we know planets at comparable distances from the star are not that rare, and we know H20 is plentiful in space. The problem is one of detection. The smaller the planet, the harder it is to detect water, so most of what we've found so far is gassy giants.
A good analogy is the fact that I don't know anyone who shares my birthday. That doesn't mean I would be amazed if I were to find someone did share my birthday, cuz I have no reason to suspect my birthday is particularly rare. I just don't know that many people.
In this case N=2 is very different from N=1. The probability of detecting further Earth-like planets is not influenced by the existence of Earth, because what we're actually measuring is the conditional probability of detecting Earth-like planets given the existence of Earth, which already factors Earth in. In this case N=1 is a lot more like N=0 and N=2 is a lot more like N=1.
That's silly. The type of world we're interested in is ones that could support life as we know it. We knew one of those exists. We're trying to find more.
Calling it silly seems a bit harsh, it's just statistics. We are interested in knowing the frequency of earth-like planets existing. If we assume that the existence of earth is a pre-condition for life existing and performing the measurement, then the existence of earth tells us nothing about that frequency. Regardless of the frequency in question the count of earth-like planets starts at 1, because in scenarios where the count is at 0 the measurement is not being performed. There could be millions of earth-like planets in the milky way, or there could be only one, or earth could even be the only life-supporting planet in the universe. There is no mechanism given only the existence of earth to reason statistically about the distribution of earth-like planets.
Whereas finding a second one tells us a lot. So that's why I say we are in more like the N=0 case, and that finding a second earth-like planet puts us in the N=1 case.
