Extract the path component of the URL with urlparse:
>>> import urlparse
>>> path = urlparse.urlparse('http://www.example.com/hithere/something/else').path
>>> path
'/hithere/something/else'
Split the path into components with os.path.split:
>>> import os.path
>>> os.path.split(path)
('/hithere/something', 'else')
The dirname and basename functions give you the two pieces of the split; perhaps use dirname in a while loop:
>>> while os.path.dirname(path) != "https://stackoverflow.com/":
... path = os.path.dirname(path)
...
>>> path
'/hithere'