So this is asking to find

So break it down. We try to work this stuff out into independent events so that we can calculate the pieces.

Standard equality for conditional probability:

Break numerator into disjoint sets.

Now that is fixed in the two summands, you can write the expressions as what happens to and what happens to separately.

Now we have "and"'s between independent events.

Now everything is standard Poisson which you should be able to calculate.