Transfering files without first formatting hard drive

I am the owner of a Playstation 3 which recently broke. After fixing that issue, I needed to figure out a way to get my hard drive to work in my new playstation without formatting and losing all of my data. So I purchased a hard drive enclosure hoping to be able to transfer these files on to my computer hard drive via the usb connection. Now the issue is that I cannot do so without first formatting or initializing my playstation hard drive. Any suggestions?

In order for me to proceed it requires me to format the hard drive. The program I am using recognizes that the drive is there however it then states "the drive is not formatted... would you like to format it the drive?" I then select no and it returns to the previous screen.