Probability Poisson Distribution

I just got a question in my exercise book that I tried to attempt but continually got the wrong answer. I am asking here to see if it was my problem or the books. The question is really quite simple:

Y is distributed as a poisson distribution. When m = 2.7 (mean) find $\displaystyle P(X<=4|X>=2)$

I thought it would just be the probability of $\displaystyle P(X=2) + P(X=3) + P(X=4)$ as all events are independent. However, this is not the correct answer.

I tried to do it using the formula for conditional probability but of course as they are independent this did not work.

A progression of the solution would be appreciated.

Cheers

Qwertyuiop23