Generally speaking, you touched on a sensitive subject. But it also depends on the relationship you have with the individual. Do you have a friendship with that person that extends beyond work hours? Has he confided in you before about his personal problems? Is there a rapport of trust and openness established between you two?

If the relationship is confined to the workplace and you are not close to the person, I think it's safe not to ask personal questions beyond what the other person volunteers to share. It is possible that your co-worker just got lucky. Your boss could have said "none of your business" to his question too. But the difference may be the following:

People generally love their kids and their current partner, but ex is usually associated with something negative (i.e. divorce). Maybe you can ask a very general and positive question, like how old is your little one?