Is it that innocent looking puddle? Still, a water puddle, per se, shouldn't make normal outdoors stairs surface slippery at all, as long as the water doesn't freeze. Frozen, the puddle would obviously be deadly.
@Kaarme
It's more the combination of fast movement + wet surface that invokes hydroplaning (followed by a tumble, then a possible sharp neck-focused impact with the stair).
For some reason it reminds me of when Spongebob finally got into the Salty Spitoon but you just see a hardcut to an ambulance because he slipped on an ice cube