We know for a normal distribution that $${ \left( n-1 \right) s^2 \over \sigma^2} \sim \chi^2_{n-1} $$

For the values you have of $n$ and $\sigma^2,$ that means $$s^2 \sim \textrm{Gamma} \left(7,\frac{100}{7} \right) $$

Now checking the CDF for this gamma random variable, $$P[s^2 < 4]=2.096444E-08,$$ which is about 1 in 47,699,809

We know for a normal distribution that $${ \left( n-1 \right) s^2 \over \sigma^2} \sim \chi^2_{n-1} $$

Equivalently (since a chi-squared distribution is a gamma distribution), we can say that $${ \left( n-1 \right) s^2 \over \sigma^2} \sim \textrm{Gamma} \left( \frac{n-1}{2},2 \right) .$$

Now if $X \sim \textrm{Gamma} \left( \alpha, \beta \right) ,$ then $kX \sim \textrm{Gamma} \left( \alpha, k \beta \right) $

Therefore $$ s^2 \sim \textrm{Gamma} \left( \frac{n-1}{2},\frac{2 \sigma^2}{n-1} \right)$$

For the values you have of $n$ and $\sigma^2,$ that means $$s^2 \sim \textrm{Gamma} \left(7,\frac{100}{7} \right) $$

Now checking the CDF for this gamma random variable, $$P[s^2 < 4]=2.096444E-08,$$ which is about 1 in 47,699,809