Though probity sounds like what you might do with a sharp stick, it actually means being morally and ethically above reproach, having integrity.
If you show fiscal probity, it means you are responsible and ethical with your money. The story of George Washington chopping down the cherry tree and refusing to lie about it is a story of probity. The story was first told by a pastor, who may have made the whole thing up according to today's scholars, possibly to sell books –– no act of probity.