This dialogue does not sound very natural because the important information inquired about by A is "new". There was a floor before the one being currently put in. Nobody would say "we're putting in the floor" here because it makes it sound as if there hadn't been a floor there in the first place. On the other hand, A could enquire "What are you going to do next?" and B could reply "We are going to put the floor in next" - here you have a first mention with a definite article because a room only has one floor and the type of floor is not important.
To tell you the truth, I never noticed how damn difficult the correct usage of articles is before I met Russians trying to come to terms with the concept.No matter how hard I try to explain all the shades of meaning conveyed by the articles, I never seem to be able to define them fully and clearly. You have my sympathies.
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