Say I'm in circumstance X and believe Y, and you're in X' and believe Y'..

I can try to understand what evidence you have for Y' -- that is, try to understand the subset of your experience of X' that is relevant to believing Y'. I can then use that understanding as additional evidence that informs my estimates of the likelihood of Y and Y'.

Or I can decide that I don't feel like putting that much effort into the question. Which is perfectly valid... as you say, this comes up all the time, and one has to prioritize.

In that second case, I can take various shortcuts.

Indeed, many such shortcuts are wired into my brain, and they aren't necessarily bad ones -- though of course experienced deceivers are used to subverting them. Others can be learned, either implicitly or explicitly. Some are so unreliable in the modern world I do best to unlearn them.

What I try not to do is fool myself into thinking I've actually evaluated the situation when I've merely taken a shortcut. If I'm dismissing Y' and reaffirming my belief in Y without doing the analysis, the alarm goes off to remind me that no, that's not justified. Y is my current belief, and I'm choosing not to investigate Y' because I've got better things to do, and that's really all I can legitimately say.