For $\alpha, \beta, z \in \mathbb{C}$ and $\lambda > 1$, if $\sqrt{\lambda - 1}$ is the radius of the circle $|z - \alpha|^{2} + |z - \beta|^{2} = 2\lambda$, then $|\alpha - \beta|$ is equal to $\_\_\_\_$.
For $\alpha, \beta, z \in \mathbb{C}$ and $\lambda > 1$, if $\sqrt{\lambda - 1}$ is the radius of the circle $|z - \alpha|^{2} + |z - \beta|^{2} = 2\lambda$, then $|\alpha - \beta|$ is equal to $\_\_\_\_$.