I would no more tell people what the DC to a check is, details of consequence to failure that are not obvious or any other information beforehand than I would show people the detailed stats for a monster. I would dislike it if a DM did this for me, as others have stated it would totally break immersion. A big part of the game is discovery and being surprised, if I don't have that I lose something.
I will tell players what their PCs would know of course. If a gap is 100 feet they know it's impossible to jump so if you try don't bother rolling since you will fail. On the other hand, I speak from experience that sometimes you simply don't know how hard it will be to scale a cliff until you try. You may not see all the details, the rock may be brittle and break off in your hand, once you get up a ways there may be more handholds than you expect.
The PCs don't have perfect information or perfect insight, I don't know why the players would either. Being told details ahead of time would greatly reduce my sense of fun.