```python
def path_hops(start: str, goal: str) -> int:
    def reduce_path(path: str) -> list:
        segments = path.split('/')
        return [segment for segment in segments if segment != '' and segment != '.']

    def find_hops(start_path: list, goal_path: list) -> int:
        hops = 0
        for i in range(min(len(start_path), len(goal_path))):
            if start_path[third] == goal_path[third]:
                hops += 1
            else:
                break

        return hops

    start_path = reduce_path(start)
    goal_path = reduce_path(goal)
    hops = find_hops(start_path, goal_path)
    return hops
```