题目分析：

一层一层，从里到外计算：~$\frac{1}{3-\frac{1}{3-\frac{1}{3-1}}}$~ = ~$\frac{1}{3-\frac{1}{3-\frac{1}{2}}}$~ = ~$\frac{1}{3-\frac{1}{\frac{5}{2}}}$~ = ~$\frac{1}{3-\frac{2}{5}}$~ = ~$\frac{1}{\frac{13}{5}}$~ = ~$\frac{5}{13}$~.

综上：答案就是B.

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