$\exp\left \{ \frac{-2\pi^2\lambda_p s^{\frac{2}{\alpha}}}{{\alpha \sin\frac{2\pi}{\alpha}}} \right \}$: Laplace to CDF

I am reading a journal paper and this is where I got stuck. I know some manipulations are involved here. My question is how do I move from the Laplace transform straight to the CDF for this equation as shown in the attached figure.

enter image description here