Let \Gamma_{1}, \Gamma_{2}, \Gamma_{3} be three pairwise externally tangent circles with radii 1,2,3, respectively. A circle passes through the centers of \Gamma_{2} and \Gamma_{3} and is externally tangent to \Gamma_{1} at a point P. Suppose A and B are the centers of \Gamma_{2} and \Gamma_{3}, respectively. What is the value of \frac{P A^{2}}{P B^{2}}?