1. We are asked to simplify the expression $20 \div 10 \div 3$. 2. Division is performed from left to right. 3. First, calculate $20 \div 10 = 2$. 4. Next, divide the result by 3: $2 \div 3 = \frac{2}{3}$. 5. Therefore, the final answer is $\frac{2}{3}$.