Zero inodes even after formatting hard disk

I have an external 1Tb harddisk which due to some reason was showing following under df -i

Filesystem        Inodes   IUsed     IFree IUse% Mounted on
/dev/sdb1              0       0         0     - /media/Transcend1T

But it has lots of free space remaining. So I took its backup and formatted it with disc utility in Ubuntu. But even after that Inodes still remain zero (it shows same output on df -i).

Is this a problem? Can some filesystems always have zero inodes?

Below is the output of fdisk -l on formatted disk.

Disk /dev/sdb: 1000.2 GB, 1000204886016 bytes
255 heads, 63 sectors/track, 121601 cylinders, total 1953525168 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x0ff10b79

   Device Boot      Start         End      Blocks   Id  System
/dev/sdb1   *          64  1953520063   976760000    c  W95 FAT32 (LBA)

Formatting screenshot. I first unmount the HDD and then click the Format Volume button shown. I have also clicked Check filesystem but it didn't fix the problem.

The filesystem you are using as an example is FAT based; it does not have inodes.

Is this a problem?

no

Can some filesystems always have zero inodes?

yes (but never say never)

I checked a fat filesystem myself and df reports no inodes, though I have been successfully using it (and it is currently holding 10GB of data).