Confusion about correlation coefficient between two zero almost surely random variables

Question

Let $X=Y=0$ almost surely. Since both random variables have zero variance, $\rho_{XY}=\frac{0}{0}$. However, in the part (b) of the following theorem from Casella & Berger (2002, page 172):

it seems that $\lvert \rho_{XY} \rvert =1$ because $a$ can be any non-zero real number and $b=0$. So, which is the correct value of $\rho_{XY}$?