smc

The denominator of the probability is $6^3=216$. We are asked to find the probability that the three numbers are consecutive. The three numbers can be arranged in $6$ ways, and there are $4$ triplets of consecutive numbers from $1-6$. The probability is $\frac{6\cdot 4}{216}=\frac{24}{216}=\boxed{\frac{1}{9}}$.