What's interesting is, although we're dealing with astronomical magnitudes here, the specific numbers do matter. Suppose that someday some fancy calculation is made that determines that, in a universe of our size, the expected value of the number of planets harboring intelligent life is 0, and that the chances of one existing is 1 / 1020. Aside from the practical implications such as immediately defunding SETI, it would give rise to a real philosophical conundrum. Merely applying the anthropic principle and saying "Well of course" would be no longer quite satisfactory without postulating an infinite multiverse.
On the other hand, if we realize that the universe with all its stars and galaxies is expected to be dotted with many billions of planets harboring intelligent life, then anthropic principle retains its original validity: that however improbable my specfic poker hand is, it's my hand. We are observing the universe from our planet, and there's nothing special about the fact that such a planet exists in the first place, as there is nothing special about the fact of holding a poker hand considering you sat down to play some fucking poker.