halacha - Can a Gentile shovel / plow snow from your driveway on Shabbat if he has been paid for general work?

I read in Kitzur Shulcah Aruch (סימן צ - דין עשית חפציו בלא מלאכה ומלאכה על ידי גוי) that even if a person prepays a Gentile before Shabbat, he cannot tell him to specifically do work for him specifically on Shabbat. There is a rule that a Gentile cannot do work specifically for you without having some benefit for himself.

Let's say you tell the Gentile, "I am paying you a flat fee for the winter season. Whenever there is a lot of snow, I want you to shovel or plow my driveway." It snows on Shabbat. Can the Gentile shovel or plow your driveway in this situation? He gains no personal benefit from shovelling the snow, but, in this case, you did not specifically say that he must come and work on Shabbat, either. He showed up because it happened to snow that day.