What is the percentage of chance a Tree Ent will spawn when a tree is chopped down?
Solution 1:
http://dont-starve-game.wikia.com/wiki/Treeguard
Treeguards do not normally spawn before Day 3, after which each Evergreen at any stage fallen has a 1.33% chance of spawning one from a nearby Evergreen tree. After Day 30, up to two Treeguards may spawn at once, with up to three spawning after Day 80 given enough Evergreens nearby.
I assume you meant Treeguards not Tree Ents. You should never feel safe, RNG is never on your side.