A rectangular floor measures $a$ by $b$ feet, where $a$ and $b$ are positive integers with $b>a$. An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width $1$ foot around the painted rectangle and occupies two-thirds of the area of the entire floor. How many possibilities are there for the ordered pair $(a,b)$?