Structural Concrete Stair Crack
This is not an uncommon crack in a concrete
stairway like this. The walls on each side of the stairs are formed to
fill up with concrete and often there is dirt filled into the center of
these forms as fill.
What happens over time is the dirt will start to compact and leave gaps underneath the stairway, these gaps over time will put additional pressure on the side walls and this could cause them to crack.
The concrete stairway could crack because this is also a weak point of the stairway. The top of the concrete stairs, that you will be walking on is usually 4 to 6 inches thick at the smallest point.
There's a good chance the crack that you're looking at is the thickness of the stairway, above the fill.
This is a structural crack and there is very little you can do about it. I would not replace the stairway until it started to become a safety issue.