The process of looking only at rows in the table where Smoke = 1 is called conditioning on a variable. Likewise, we say that Fire and Alarm are conditionally independent, given the value of Smoke. This is important to know if you are programming a machine to update its beliefs; conditional independence gives the machine a license to focus on the relevant information and disregard the rest. We all need this kind of license in our everyday thinking, or else we will spend all our time chasing false signals.
