This is a version of the Monte Hall paradox. At the beginning of the show the contestants randomly select the boxes. There are 21 chances of picking a box without £250,000 and 1 chance of picking the £250,000 box. So the chance of the contestant having the big one are slight. Although somebody must have it. The perceived wisdom is to change. Type "Monte Hall" into a search engine to get a fuller explanation.
The contestant did not exchange and walked off with £75,000. No small amount, but she could have trotted off with £125,000. Greed reared it's ugly head.
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