We had a situation like this in November at the hotel where we were staying. The fire alarm started ringing at 4 am. I always keep my 'must have this' stuff right beside the bed when I travel. I grabbed my glasses, shoved my phone and its charger into my purse, slipped on shoes & a jacket while my other half was grabbing his shoes, wallet, glasses & jacket. The fire stairs were less than 10 feet from our room. We went down all twelve flights and waited outside until the fire department came and did their thing and said it was all clear.

Apparently there had been smoke two floors below ours, but it wasn't anything major. I know that because we asked at the front desk later in the day. We didn't ask for anything. (We weren't offered anything, either.) I was just glad that their smoke detectors worked well.