My boyfriend and I live in an old house with a very narrow stairway and treads that aren't long enough to actually get your whole foot on them. To make matters worse, one of the treads is broken, with the whole outside edge pushed down to the stair below, leaving almost nowhere to step. We've had multiple people, including me, place their foot wrong and go tumbling down them, but we're a bit intimidated by both the potential cost and labor that might await us. There is old carpet covering the stairs, so while we know that one tread is broken, there's no telling what else might be awaiting us.
We have some experience with home improvement and carpentry, so my question is, how difficult would it be, assuming the rest of the stairs are sound when we pull the carpet up, to go in and fix the one stair, and widen all the treads to accommodate modern feet and stop the falls? Is it just a matter of retrofitting the current setup, or is it more a matter of ripping out the entire staircase and starting from scratch?