This can be written as a function indexes() and then take the max() of the resulting iterator:
Example:
def indexes(xs, value):
    for i, x in enumerate(xs):
        if x == value:
            yield i
a = [2, 2, 4, 2, 5, 7]
print max(indexes(a, min(a)))  # 3
Update; Just as a matter of completeness; if you per se wanted the minimum index for a set of values with more than one minimum you'd just swap out max() for min() at the front of the expression. So:
a = [2, 2, 1, 4, 2, 1, 5, 7]
print min(indexes(a, min(a)))  # 2
whilst:
print max(indexes(a, min(a)))  # 5
This is kind of handy and flexible in general :)