Poisson Distribution - Conditional Probability Question I have come across a question in my notes and I do not understand how to solve it. I have looked at the solutions and I still am unclear!
This is the question:

And this is the solution:

I really don't understand what the question is really asking - would anyone be able to explain to me with an example? I also don't understand what the implication of the conditional probability is: e.g. the prob of 1 goal being scored given that 1 or more goals have already been scored? But then that should be independent?
Sorry - again, I am very confused and any help would be much appreciated!

The question has asked, given $N\sim\textrm{Poi}(\lambda), $ to find the value of $\lambda$ such that $\mathbb P[N=1|N\geq 1]= 0.4.$
The solution is nothing but applying the definition of conditional probability and Poisson distribution:
\begin{align}\mathbb P[N=1|N\geq 1]&=\frac{\mathbb P[(N=1)\cap(N\geq 1)]}{\mathbb P[N\geq 1]}\\&= \frac{\mathbb P[N=1]}{\mathbb P[N\geq 1]}\\&= \frac{\frac{e^{-\lambda}\lambda^1}{1!}}{1-\mathbb P[N=0]}\\&=\frac{\lambda e^{-\lambda}}{1-e^{-\lambda}}.\tag 1\label 1\end{align} Equate $\eqref 1$ with $0.4$ and find the value of $\lambda.$
