I had a decent amount of spies convert in a recent game. The opposition had plenty of provinces but I believe what caused them to swap was that the player went all out. My espionage report stated they had about 2mill cash (Antartica match) and the player later told me he had sent over 200 spies my way.
In experimenting with spy mechanics, I moved my ground units off the control point of all provinces and set all aircraft to patrol. I also redeployed the 60-ish I had in the field to CE. In the end, I lost all of my aircraft, a small amount of ground units (most were higher ranked) and I had roughly 110ish spies after 36-48 hours. I lost some structures/infrastructure but with it being dominion, I had built everything to cap in the provinces that were protected.
I think the spies converted because there wasn't enough cash available for their maintenance.
So, more direct to your question. I had Counter Espionage spies in the provinces where I was being spied on. Their home nation couldn't afford to pay them so they agreed to join.
