"The juice is ours."
Translation:O suco é nosso.
Can't help you with any rules, but you wouldn't say that. Probably because "suco" and "nosso" refer to the same thing, so you're repeating the article for no reason. However, if you were pointing out your juice from other people's juices, you would say "This is ours" > "Este é o nosso", "o" not being mandatory, but most naturally to be used here.