Ever tried to "read" braille? I can't make out a thing... but a skilled reader of braille can simply run their finger tips over the "writing" as significant speed and read it perfectly. While I don't think the blind person can "visualise" the raised surfaces, what is clear is that they have a highly developed spacial mapping.
While I doubt you or I could ever understand fully the detail of the mapping, I think you can get the idea of how it works... after all when playing a synth or even typing on the keyboard in front of you or driving a car, you don't need to think about the spacial relationships involved you have a natural ability to co-ordinate without really thinking.
I imagine a blind person simply has a finer grained version of that... because we can use our eyes we never think of it as a two way system, but it is.
As a fun experiment blindfold yourself for a week and see how you get on around your house? :-)
Interestingly the part of the brain that deals with spatial relationships is located right next to the visual cortex... The human brain has been well documented in it's ability to reorganise due to damage, especially in neighbouring areas... if the visual cortex is unstimulated I'm sure it will reassign to assist more demanded areas.
Oh, and I bet A.org is a barrel of laughs for a blind person... :-(