jmc

There are $5$ options for the last digit as the integer must be odd. The first digit now has $8$ options left (it can't be $0$ or the same as the last digit). The second digit also has $8$ options left (it can't be the same as the first or last digit). Finally, the third digit has $7$ options (it can't be the same as the three digits that are already chosen). Since there are $9,000$ total integers, our answer is $$\frac{8\cdot 8\cdot 7\cdot 5}{9000}=\boxed{\frac{56}{225}}.$$