<image> As shown in the figure, \( P \) is a point outside the plane of triangle \( ABC \). The plane \( \alpha \) is parallel to the plane \( ABC \). The plane \( \alpha \) intersects the line segments \( PA \), \( PB \), and \( PC \) at \( A' \), \( B' \), and \( C' \) respectively. If \( PA' : AA' = 3:4 \), then find the ratio \( S_{\triangle A'B'C'} : S_{\triangle ABC} \) = ______ .