Probability that a random matrix built from two binomial variables is orthogonal

Let $X$ and $Y$ be independent $\mathrm{Bin}\left(3,\frac13\right)$ random variables. Then the probability that the matrix

$$P=\begin{pmatrix}\frac X{\sqrt2}&\frac Y{\sqrt2}\\-\frac1{\sqrt2}&\frac1{\sqrt2}\end{pmatrix}$$

is orthogonal, is