This is a person with whom you may be making some very important decisions. So, it may be less important what the candidate thinks than how they think. To understand more about the candidate's thought processes, talk to them as you would to a new friend. Don't just ask about their accomplishments and goals, but about what makes them tick. Ultimately, the goal is to find out if your personalities are compatible.
Competence is a given.
At this stage, each candidate has survived an extremely rigorous elimination process. So, you don't have to dwell on what they did at the XYZ Corporation back in 19eightysomething. You should have a full report in front of you that tells you exactly why and how they are completely qualified. In order to really learn how the candidates operate, you need to pay close attention to things like ethics, presentation style, method of thinking, creativity, and of course, chemistry. You are also being interviewed.