6. Choose three different numbers from $1,2, \cdots, 10$.

Then the probability that these three numbers form an arithmetic sequence is $\qquad$
6. $\frac{1}{6}$.

Let the three numbers drawn be $a>b>c$. From the problem, we know that $a$ and $c$ have the same parity. Therefore, $p=\frac{\mathrm{C}_{5}^{2}+\mathrm{C}_{5}^{2}}{\mathrm{C}_{10}^{3}}=\frac{20}{120}=\frac{1}{6}$.