In Srednicki's Quantum Field Theory chapter 11, the probability of a $2 \to n$ scattering process is calculated to be
$$ P = \frac{|\left<f|i\right>|^2}{\left<f|f\right>\left<i|i\right>} = \frac{(2\pi)^4 \delta\left(k_1+k_2-\sum {k'}_i\right) T}{2E_1 2E_2 V} |\mathcal{T}|^2\prod_{i'} \widetilde{dk}_i'.\tag{11.11+20} $$
He then proceeds to divide this by $T$ to obtain a probability per unit time, before yielding an expression for the differential cross section. However, the factor of $T$ is troubling me: as $T\rightarrow \infty$, $P$ is going to exceed $1$ at some point, isn't it? Does this have to do with dealing with plane waves instead of wave packets? I am aware that this problem also shows up when one uses Fermi's golden rule to calculate decay rates, but I guess I never thought about it too seriously then.