The narrator is most likely omniscient. In this case, the narrator knows that there is only one staircase leading to the floor above, so they would probably use "the". It may also be acceptable to use "a", but I would prefer "the".
If the narrator was not omnisient, for example it was Jack's friend Bob, then they would use whatever word they believe is most appropriate based on what they know or believe or assume to be the case.
It doesn't matter what the reader knows.
Suppose you had no idea of what your surroundings were, and you had your eyes closed. In this case, I could say "Look at the sheep", if I wanted you to look at the specific sheep that I knew was there. Alternatively, I could say "Look at a sheep", if I just wanted you to look at any sheep. It doesn't matter that you don't know what your surroundings are, I can use either phrase to convey whichever meaning I want.
After all, the speaker doesn't always know what the person listening knows, so they can't reliably change their speech to adjust for that fact.
Edit: my confidence in this answer has decreased, after realising that "He came across a monster. The monster spoke to him." Is more natural than another choice of articles, even though the narrator clearly knows that there is one monster, and to him, it is clear what monster he is talking about, which is something that my explanation fails to take into account. In this case, what matters isn't so much what the speaker knows or what the listener knows, but rather whether or not it is clear that the speaker is referring to. Because it is initially unclear what monster the speaker is referring to, initially "a" is used, but later, it is clear what monster the speaker is referring to, so "the" is used.
I have spent too long thinking about this and don't want to spend more time thinking about it, and am not confident that my answer is perfect, but also believe that my answer has potentially valuable information that I don't want to delete.
Edit: I just found out that the difference between the definite article in English and the specific article in Samoan is that the definite article in English cares about whether the listener would be expected to know which specific referents are intended, whereas the specific article in Samoan only cares about whether the the speaker has a specific referent in mind. So I suppose it does matter what the listener is expected to be able to know, after all.