If the goal is to make the conversation interesting/smart, it starts with great difficulty because what sounds interesting/smart to one may be just dull/stupid to another.
Most people may feel a little reluctant when someone else is digging, but that is only because they have grown an instinct to honestly disbelieve anyone may be truly interested in knowing them for nothing.
Since we can't worry how people feel about our little inquiries, we can only ask and be honestly interested in knowing more about others, discovering more.