Example 3. As shown in the figure, in $\triangle ABC$, $DE \parallel BC$, and $S_{\triangle ADE} : S_{\triangle CDE} = 1: 3$. Find the value of $S_{\triangle ADE} : S_{\triangle CDS}$. (1990, Sichuan Province Junior High School Mathematics Joint Competition)
Analyzing, it is known that $S_{\triangle C D E}$ is three times $S_{\triangle A D E}$. According to the problem, it is actually only necessary to find out how many times $S_{\triangle C D B}$ is of $S_{\triangle A D K}$. From the given information, we can get $\frac{A E}{E C}=\frac{1}{3}$, and $\because D E / /$ thus the required ratio is $\frac{1}{12}$.