Probity is integrity, but more. Probity is honesty, but in a form more related to trustworthiness.
When a person has probity, it is easy for others to trust his words and to have faith in his judgement.
Buddha said: "Do not believe in anything simply because you have heard it. Do not believe in traditions because they have been handed down for many generations. Do not believe in anything because it is spoken and rumored by many. Do not believe in anything simply because it is found written in your religious books. Do not believe in anything merely on the authority of your teachers and elders. But after observation and analysis, when you find that anything agrees with reason, and is conducive to the good and benefit of one and all, then accept it and live up to it."