What is the religious ruling on a divorce that occurred with the phrase "you are divorced by three" after the wife was told, "if you tell him, it is by your word" and "if you leave while we are quarreling, then you are divorced by three," given that she did leave, even though she was not angry?

The majority of scholars hold that a conditional divorce takes effect if the condition is met, and that a triple divorce pronounced as "three" counts as three. Accordingly, the divorces you mentioned have taken effect in all three instances. In the first instance, the divorce occurred with your statement "she is your word [divorced]." In the second instance, a triple divorce occurred if you intended to prevent her from leaving after the quarrel, regardless of her condition. As for the last instance, a triple divorce occurred with your explicit declaration. Consequently, your wife has become irrevocably divorced from you with a major separation (baynunah kubra), and she is not lawful for you unless she marries another husband willingly, and then he divorces her, and her waiting period (iddah) expires.