Focusing on the defects of famous defogging algorithms for fog images based on the atmosphere scattering model, we find that it is necessary to obtain accurate transmission map that can reflect the real depths both in large depth and close range. And it is hard to tackle this with just one prior because of the differences between the large depth and close range in foggy images. Hence, we propose a novel prior that simplifies the solution of transmission map by transferring coefficient, called saturation prior. Then, under the Random Walk model, we constrain the transferring coefficient with the color attenuation prior that can obtain good transmission map in large depth regions. More importantly, we design a regularization weight to balance the influences of saturation prior and color attenuation prior to the transferring coefficient. Experimental results demonstrate that the proposed defogging method outperforms the state-of-art image defogging methods based on single prior in terms of details restoring and color preserving.