I will be interested but not intrusive
Often times when colleagues relate with each other they cross the line of intrusion without even knowing it. This is because with the dynamic nature of people, what constitutes an intrusion to one differs from the other- But we have classic examples like family, relationships, financial position, health etc. These examples are real issues that the working class deal with. To avoid being intrusive, your sure bet is not to ask questions bordering on these areas until the person involved offers to share. When they eventually do, show genuine interest, which implicates that once they become uncomfortable with the discussion, you may wish to end it. Intrusion ranks as a key cause of workplace conflict, while genuine interest fosters a congenial workplace.
Have a conflict free work environment...