Probability a random matrix is orthogonal

Consider the matrix $$A=\begin{pmatrix}X_{11}&X_{12}&X_{13}\\X_{21}&X_{22}&X_{23}\\X_{31}&X_{32}&X_{33}\end{pmatrix},$$ where $X_{ij}$, $1\le i,j\le 3$, are independent and identically distributed random variables with the probability mass function $$f(x)=\begin{cases}\frac{1}{3},&x=-1,0,1,\\0,&\text{otherwise.}\end{cases}$$ The probability that $A$ is orthogonal equals