He expects that the conflict will start with the Vulcans complaining about the disparity in their large population size and small space of their territory to the Sun King.
After that, he predicts that the Sun King will then ask the Snow King for more space to expand the territory of the Vulcans.
Arthur is willing to give the Sun King some grace and say that the Sun King will ask for more space politely. But he also knows that no matter how polite the Sun King is about it, the Snow King won't listen to him and will reject his request.
He expects the Snow King to say, "The space we have is what we fought for. We need it to expand our population. If we don't have a large space, how can my people prosper?"
This will anger the Sun King, who will then say, "Since you fought for this space, why don't I fight you for it?"
And so a war will happen.
