It is safe to assume that he figures when he went in a 100 year old tree was there and unless suddenly people decided to bulldoze the trees down indiscriminately that it was probably still there as an old tree that has survived as long as it has. At the end of the day though, he did't know if they had cut the tree down or not, he was going on faith that it was still there like it was when he went in. Its more of the symbolism of something enduring like an old solitary tree that is there year in year out and long after we come and gone.
Update
In Stephen King's manuscript, the tree occupied a field in Buxton, Maine, but in real life the scene was shot 810 miles away in Richland County, Ohio.
Five years ago, lightning hit the oak and some of the tree was damaged. Jodie Snavely with the Mansfield & Richland County Convention and Visitors Bureau says the rest of the tree fell Friday due to high winds. "It's a sad day for Shawshank fans," she said.
Thanks to the film, the field and tree have become an international tourist destination.
SOURCE: CNN 02/22/2016
UPDATE 2
What remained of a 200-year-old oak tree made famous by the movie
"Shawshank Redemption" has been cut up and hauled away by an owner of
the north-central Ohio property.
The Mansfield News-Journal reports (http://ohne.ws/2ohFpuC ) Dan Dees
said last week he plans to use some of the wood to make a table. The
tree was rotted in the middle when high winds knocked down a portion
in 2011. It was further damaged during a storm last July.
SOURCE: MSN 04/08/2017