The conjecture "if a > b, then a/b > 0" is actually correct. When a is greater than b (a > b), and both a and b are positive, zero, or negative, the result of dividing a by b (a/b) will always be greater than zero (a/b > 0). This is a fundamental property of division.
There are no counterexamples to this conjecture within the specified conditions. If a > b, then a/b will be greater than zero as long as a and b have the same sign (both positive or both negative) or if b is zero.
However, if a > b and a is positive while b is negative, then a/b will be negative. This is not a counterexample to the conjecture because the conjecture specifies that a and b are both greater than zero.