There are no qualifiers on the "circumstance" in the spell, and "circumstance" is an awfully broad term in plain English. It can mean literally the things around you, or metaphorically so, or it can be anything which is connected to and influences another thing.
1a: a condition, fact, or event accompanying, conditioning, or determining another
In the case of the spell, the "another" is the contingent spell. So, the "circumstance" is any condition, fact, or event that you by the magic of this spell link to the activation of that other spell. (That is, you describe a condition, fact, or event which — in this case — determines the activation of other.)
This leaves the DM to determine exactly what is a reasonable trigger; it is a 6th-level spell, which is fairly powerful, but not invincible. I'd look to true seeing (also 6th level) and scrying (5th) for some bounds to reasonableness.
Of course, it's also worth consider the example given — water breathing "when you are engulfed in water or a similar liquid" — which is clearly both local and immediate. There's no clear requirement of that, though, and as a DM I'd allow it to work based on things that happen far away. Having something happen when a wizard's lab is invaded, or sure, notifies the suspicious grand vizier when the king dies seems fun for story to me. And, it's still got an expensive component (even if not consumed), along with the opportunity cost of not allowing another more immediate contingency to be active.
On the other hand, I wouldn't allow probing broad truths of the metaverse by testing if facts are, indeed, facts — not by any particular rule but just because that seems out of scope. However, there's definitely room in the spell for another DM to rule more broadly.