Adding custom path by updating ~/.profile with not working

Don't use a space before or after = when you assign a value to a variable in bash. The right way is:

PATH="/user/share/android-sdk-linux/tools:$PATH"

For the changes to take effect, restart your computer or source your .profile file using the following command:

source ~/.profile

If you want to change the path for all users, add that line in /etc/profile file. Again a restart is required.

If I understood correctly you want to permanently change the value of the PATH envar.
In Ubuntu the PATH envar is defined inside the /etc/environment file. So you need to modify the PATH envar declaration inside that file, not inside the .profile!
Use this only if you want to change the PATH value for every users!