Same problem was happening to me as mentioned by OP.

Howsoever after doing the following steps it worked like charm: -

> 1) Do these steps as mentioned in this video [here.][1] (Follow this
> video till 50 second mark) (Basically you have to delete the `.inProgress` File and `reboot` your computer.)
> 
> 2) Now before connecting your external HDD for backup, go to terminal
> and execute the following code as mentioned in [this][2] answer. (i.e. Disable spotlight) (Execute **only** the first line of code)
> 
> 3) Now connect your external HDD with your computer and start the
> backup.

Now please have patience, give it around `30 minutes`.

Even now if the backup is still stuck on "Preparing backup" then: - 

> Execute the second line of code given in the above linked answer (That is,
> enable the spotlight again) **While "Preparing for backup" is still
> running** .


Now in my case I waited for `45 minutes` after following the above steps and then finally my Mac started its backup.
 


  [1]: https://www.youtube.com/embed/KvxZJLEi-UM?start=0&end=50
  [2]: https://apple.stackexchange.com/a/312200/389538