A forest consists of $3$ types of trees: $30\%$ are oak, $50\%$ poplar, and $20\%$ are beech. Following a storm, an illness develops and affects $10\%$ of the oaks, $4\%$ of the poplars and $25\%$ of the beeches.

Knowing that a tree is sick:

What is the probability that it is an oak tree?