1. **State the problem:** Simplify the expression $$1 - \frac{\frac{1}{2} - 3}{1 - \frac{1}{4} \div \left(1 - \frac{1}{3}\right)}$$. 2. **Simplify the numerator:** Calculate $$\frac{1}{2} - 3$$. $$\frac{1}{2} - 3 = \frac{1}{2} - \frac{6}{2} = -\frac{5}{2}$$. 3. **Simplify the denominator:** First simplify the inner parentheses: $$1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$$. 4. **Calculate the division inside the denominator:** $$\frac{1}{4} \div \frac{2}{3} = \frac{1}{4} \times \frac{3}{2} = \frac{3}{8}$$. 5. **Complete the denominator:** $$1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}$$. 6. **Rewrite the original expression:** $$1 - \frac{-\frac{5}{2}}{\frac{5}{8}}$$. 7. **Simplify the fraction inside:** $$\frac{-\frac{5}{2}}{\frac{5}{8}} = -\frac{5}{2} \times \frac{8}{5} = -4$$. 8. **Final calculation:** $$1 - (-4) = 1 + 4 = 5$$. **Answer:** The value of the expression is $$5$$.