Raven Idol > Innovate

So the numbers come out so that you can simply divide the number of spells you can chose from into the number of spells that are there; which comes out 3/27 = 1/9 comfortably.

So why does this other method work?

Simply put: it's to do with the way it cancels when you inspect the positions in the discovered cards from left to right:

The first slot has 1/27 to Innovate.  If it's not Innovate, 26/27 of the time, we look at the second slot
The second slot then has 26/27 * 1/26 to Innovate.  This term reduces to 1/27.
Likewise the 3rd slot has a chance of being relevent: if the first slot AND the second slot are both not Innovate:  this is equal to 26/27 * 25/26 * 1/25, which reduces to 1/27.

So by counting across slots we have 
P(nnovate) = 1/27 + 26/27*1/26 + 26/27*25/26*1/25 = 3*1/27 = 1/9