A very difficult subject and with no definitive answers. Everyone behaves differently.

A simple "how are you doing" will solicit a simple okay thank you, or they may perceive it that you are inviting them to talk more. There are so many comments that people make that are inappropriate. I remember my late neighbour saying when her son died, she received lots of cards with the printed message "when one door closes, another opens". Now that is inappropriate, as it's usually associated with a person getting a new job or moving to a new city, not a death.

How they respond is their coping mechanism. Don't feel slighted by their behaviour. The event may have also stirred lots of unhappy memories.