(of course you need to adjust the path to your drive), and then give the group write permission:
sudo chmod -R g=rwx /mnt/my_mounted_drive/
And one word of caution: in your example you are sharing a notebook. As all users access the same file, it will create an absolute mess when they all open and modify that notebook. This is why usually users don’t get write access on such a shared location.
Though the command is: sudo chown -R root:jupyterhub-users /mnt/my_mounted_drive/
I used this for my shared data drive, but created a shared code folder where only I have rwx access and all others only have rx access with this command: sudo chown -R jupyter-mtrl_scientist code
This avoids the problem you mentioned where multiple people have write access to the same notebooks.