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Dumbledore is a decent mind reader iirc but Snape was the OG. He didn’t need to read Harry’s mind, he cast the spells on the cup and knew Harry wouldn’t have been able to get his name in there and that someone else had to do it.
As I recall (it’s been a while) you have that backwards, Snape was the OG at blocking mind reading, but only reasonably proficient at doing it himself, whereas Dumbledore was able to weedle memories out of people that they didn’t even know they had
That sounds more right