def levelize_path(path):
    """Splits given path to list of paths removing latest level in each step.
    
    >>> path = '/application/item/new'
    >>> levelize_path(path)
    ['/application/item/new', '/application/item', '/application']
    """
    parts = path.rstrip('/').split('/')
    paths = []
    for i in range(len(parts), 0, -1):
        sub_path = '/'.join(parts[:i])
        if sub_path:
            paths.append(sub_path)
    return paths
