HMMT November 2022 U2

The English alphabet, which has 26 letters, is randomly permuted. Let $p_{1}$ be the probability that $\mathrm{AB}, \mathrm{CD}$, and EF all appear as contiguous substrings. Let $p_{2}$ be the probability that ABC and DEF both appear as contiguous substrings. Compute $\frac{p_{1}}{p_{2}}$.