Depending on the computer, if you use a Mac to do the deletions the space when doing a get info on the Mac will show the free space, but the images are still there in the recycle bin. Empty the trash with the card in the computer and they will be gone.
It is recommended however to only format the card in the camera. After down loading the images and after confirming the backup, unless they don't matter put the card in the camera and do a format. This is the best practice. That way you know the card is now empty.
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