The way I see it, the uncertainty exists prior to comparing the passive score to the DC. It's resolved once compared.
That's a bit of a stretch, for me. But, OK...
So the player has described the character undertaking an ongoing task ("I keep watch for monsters and traps as we delve...") and, based on subsequent movement and position, the DM determines if that effort has a certain or uncertain outcome by whatever standards seem appropriate.
I'm not so sure I find the 'ongoing task' criteria compelling. It doesn't quite have the same impact, to me, as an action declaration, and there are many 'ongoing tasks' that might be part and parcel of adventuring and not really need declaration - there's a whole thread about those, too.
But, if it is comparable to an action, I'd think calling for a check in the case of uncertainty would be the way to go, as being 'fair' and more engaging for the player.
....though, of course, only at the point where the consequence of failure would manifest.
If certain, there's no need to compare passive score to DC - the PC just succeeds or fails outright. If uncertain, the DM then goes to the passive score and compares it to the DC to get at an outcome.
So you could determine a PC is 'certain' to notice a trap before triggering it, even if his passive is lower than the DC to find it? Or, you could determine that it was 'uncertain' in which case he would automatically fail to find it, just as if you had decided failure was certain?
I can see the lack of certainty from the player side, because he doesn't know the DC, and still won't know it after succeeding or failing. ..OK, or maybe just lack of information... On the DM side it seems pretty certain, though.
Comparing DC to DC like that just seems to me like a quantitative way of judging whether to narrate success or failure. I can see that. I'd prefer to call for a check if they were close, though.