Today in class, my teacher was teaching determinants. He gave us problems to solve of various kinds, including various row-column operations and determinants properties. But one thing that remained common was the fact that in every other problem the value of the determinant was coming out to be $0$. It was so very frequent that the two rows came out to be common, one row/column came out to be zero and finally the answer was zero. This motivated me to put forward a question which my teacher said was too hard for my fellow classmates. Please help me with this.
Consider we have $9$ random integers chosen from the set $[0,n]$ in order. Then find the probability that in their given order these integers forms a $3 \times 3$ matrix which is singular. That is, say we choose $x_1, x_2, x_3, \dotsc, x_9$, then find the probability that $$ \begin{vmatrix} x_1 & x_2 & x_3 \\ x_4 & x_5 & x_6 \\ x_7 & x_8 & x_9 \end{vmatrix} $$ is equal to $0$.