Time machine backups not recognised after OS upgrade
The format of the backup has changed a lot between 10.6.8 and 10.9. There were several upgrades and some newer versions recognised backups from previous versions. This could be one of reasons why Apple recommends upgrades for each new OS sequentially.

If you continue backups, most likely Time Machine will do one of two:


override your current backup
create a new backup bundle


I am not sure what it chooses and when but I had both those cases happening. If you do not need old backups, just remove them. If you need them, you can move them to a subfolder.

One more solution for you could be to remove and add a Time Machine disk. Sometimes that helps Time Machine to recognise that the drive has backups. Logic of Time Machine is very strange sometimes.