It is not uncommon in a polite social life to encounter situations where literally nothing can be done (a colleague's parent dies; an acquaintance gets cancer).

It is not uncommon in a polite social life to encounter situations where literally nothing can be done (a colleague's parent dies; an acquaintance gets cancer). Yet, doing something even symbolically is required. It is therefore quite rational to be able honestly to say you will pray for someone -- even if you are atheist -- if the goal is to maximally signal support and goodwill (which you believe will benefit the "recipient" in some small but possibly positive nonzero way, as well as signaling virtue from the "sender".) Frankly, that is one major reason I have instituted prayer in my decidedly atheist household.