A grove has $6$ rows of birch trees and $5$ rows of maple trees. Each row of birch trees has $8$ trees $20$ feet or taller and $6$ trees shorter than $20$ feet. Each row of maple trees has $9$ trees $20$ feet or taller and $7$ trees shorter than $20$ feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is $20$ feet or taller?