Zanz said in chat that Miracle took up 2 of the 24 False God spaces, so there's an 8.33% chance of facing Miracle. According to the Wiki statistics, there's a 33% of winning at least 1 card from the spins after beating Miracle, and a 16.1% chance of winning an Improved Miracle.
So that's roughly a 0.44% chance of winning an Improved Miracle in that manner -- this might be a little off depending on your deck's win rate against Miracle. Not likely, but bound to happen due to the sheer number of games played as you farm the FGs.