1. **State the problem:** We need to simplify the expression $1 \frac{1}{3} - \frac{1}{3} - \frac{4}{5}$. 2. **Convert the mixed number to an improper fraction:** $$1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}$$ 3. **Rewrite the expression with improper fractions:** $$\frac{4}{3} - \frac{1}{3} - \frac{4}{5}$$ 4. **Subtract the fractions with the same denominator first:** $$\frac{4}{3} - \frac{1}{3} = \frac{4 - 1}{3} = \frac{3}{3} = 1$$ 5. **Now the expression is:** $$1 - \frac{4}{5}$$ 6. **Convert 1 to a fraction with denominator 5:** $$1 = \frac{5}{5}$$ 7. **Subtract the fractions:** $$\frac{5}{5} - \frac{4}{5} = \frac{5 - 4}{5} = \frac{1}{5}$$ 8. **Final answer:** $$\boxed{\frac{1}{5}}$$