Hm... I think there are things with one sided uncertainty, that make the ops example possible.
For example, things rarely start before they're scheduled, so if you know something is supposed to happen at 5 and last an hour, it's reasonable to assume it will be happening at 5:10, so if it's 4:59 right now, you're more certain that it will happen in 11 minutes than in one minute.
Of course, as time progresses your uncertainty curve flattens out (at 5:09 you're pretty certain it'll happen any moment now), but that's only in the future.
Even then, it's quite reasonable to say that there's no time leading up to the event where you're more confident it will start imminently than you're confident it will be occurring further out.
For example, things rarely start before they're scheduled, so if you know something is supposed to happen at 5 and last an hour, it's reasonable to assume it will be happening at 5:10, so if it's 4:59 right now, you're more certain that it will happen in 11 minutes than in one minute.
Of course, as time progresses your uncertainty curve flattens out (at 5:09 you're pretty certain it'll happen any moment now), but that's only in the future.
Even then, it's quite reasonable to say that there's no time leading up to the event where you're more confident it will start imminently than you're confident it will be occurring further out.