I believe this wording in the above news post is a bit misleading:
|Subscriptions will be $99 for the year, and it marks an interesting new turn in the website's popular Prime service.|
|No additional cost|
With Prime Music, there is no cost. You can listen to the entire Prime Music for free – it’s included with your Amazon Prime membership.
The service is included in the cost of the normal Prime membership, which is $99 a year, but also includes free shipping on Amazon products as well as their Netflix/Hulu competitor Instant service.
That alone -- that there's already an existing user base in place -- is enough give this a foothold. Add in the other benefits you get with Prime and if, obviously it's a big if, they design the UI and UX right this could be massive.