Seems like you'd have to have some sort of simple "checkout" system for a post. When any user views a certain post, it automatically "checks out" that post and no one else can see it. The tricky part, it seems to me, is checking that post back in. How do you know when someone is done looking at a post? One fairly sure way is if the user navigates to a different page, but that's not the only way, and just because someone navigates to a new page doesn't mean they didn't leave the original post open in a different tab. And what if the user viewing the post just gets up and walks away from the computer for the day, with the post still up? Or what if they leave the post open, but move onto other browsing activities?
It seems like you might need to have a way for each checkout to "expire" after a certain period of time, and maybe the user viewing the post can "renew" the post when their checkout period is about to expire.
Then, obviously, you let a user view a particular post only if it's not already checked out by someone else.
I'm happy to supply ideas regarding the nuts and bolts of how to implement such a system, but I'll save that for later in case someone else has a better conceptual idea, or in case I totally misunderstood your question.