Are the following sentences both acceptable?
When you see India, China, Korea, and Japan, you will remember that India is very far from the other three nations.
When you see India, China, Korea, and Japan, you will remember that India is very far from the three other nations.
In that sentence, there's no ambiguity. You know there are four in total, and you're talking about one compared to the other three.
However, with "the other three" in other situations, it could sound like there are two groups of three. France, Germany, and the Netherlands, compared to Malaysia, Indonesia, and Singapore, for example.
So in the original, "the three others" would actually be more accurate. My rule is that clarity is the most important rule, over "correctness" and since there is no chance at all for misunderstanding the first one, it doesn't matter that much.
But it would be good to understand the difference so you could apply it correctly in other situations.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.