Non-Transitive Dice I

Let $A,B,$ and $C$ be three fair $6-$sided dice. $A$ has the three values $2,6,$ and $7$ on two sides each. $B$ has the three values $1,5,$ and $9$ on two sides each. $C$ has the three values $3,4,$ and $8$ on two sides each. Find the probability $A$ shows a strictly higher value than $B$.