Let $\mathbb{R}$ and $\mathbb{R}^{3}$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors
\[
\left\{\left[\begin{array}{lll}
2 & -3 & \alpha
\end{array}\right], \quad\left[\begin{array}{lll}
3 & -1 & 3
\end{array}\right], \quad\left[\begin{array}{lll}
1 & -5 & 7
\end{array}\right]\right\}
\]
does not form a basis of $\mathbb{R}^{3}$ is $\_\_\_\_\_\_\_$.