Recently we found some pretty bad dry rot behind our concrete stairs. we repaired the rot and now are going to refinish the stairs as well as stucco our house. Obviously the caulking that had been injected between the house and stairs did not work, does anyone know the proper way to flash this area so this doesn't happen again?

Also, you might be able to see some yucky glue residue left over from some lovely astro-turf that was glued to the stairs, any ideas on removing that?
THanks

for some reason I can't upload the pictures but there is about a 1 in gap between the house(without siding) and the stairs.