Godwin's law applies to any subject. Replace nazi's with any other subject and it will still hold true.
That's not true. Godwin's law says that the probability that a
new post will bring up a comparison with Nazis increases. Not simply that as the sample size grows the probability of the set containing some value increases.
Which isn't always true either.
It's like saying that after flipping a coin 2 times, the probability that you flipped a heads approaches 1.
The analog for Godwin's law would be that the odds of each new coin toss increases in favor of some direction with the number of tosses that preceded it. This isn't true, regardless of how many times it was tails in the past its odds of being heads next time won't change (see gambler's fallacy, and of course this is for pure random perfect systems that don't have some systemic influence)
Coins don't have memory. The tosses are independent. Forum threads do. The posts aren't independent.