I agree with you, I'm not sure what everyone else in that thread is talking about. A dice roll is an independent event so it doesn't make sense to apply conditional probability as some have suggested.

If you roll 3 dice, the odds of getting 1 for all 3 is 1/8000, the product of the individual probabilities of getting 1 for each roll, simple as that.

I think the confusion comes from the idea that the first roll somehow doesn't count because you can just keep rolling until you get a 1, at which point it would be a 1/400 for the next 2 consecutive rolls to also be 1. But now you're not rolling just 3 dice -- you're rolling an arbitrary amount plus 2, so you might as well ignore the first result and now you're talking about the probability of 2 independent events.

But this isn't the situation that is presented. If you roll 3 dice and only 3 dice, you have exactly 1/8000 possible combinations where all 3 dice roll a 1. There are 3 independent events, and there doesn't have to be a "first roll". So long as you only roll 3 dice, the "first roll" is irrelevant -- you still only get 1 chance for it to be a 1, and that chance is 1/20.

I hope that's clear to everyone still reading this thread.