= Solution
The two indistinguishable paths to the same final state must be added as <probability amplitudes>:
$$
\mathcal A_f(t)=A_f g_+(t)+\frac qp\bar A_f g_-(t)=A_f[g_+(t)+\lambda g_-(t)].
$$
Taking the <Complex modulus>[squared modulus] gives the time-dependent <decay rate>, with the common final-state <Lorentz-invariant phase space>[phase-space] <normalization> absorbed into the <probability amplitudes>:
$$
\boxed{\Gamma(K(t)\to f)=|A_f|^2\left[|g_+|^2+|\lambda|^2|g_-|^2+2\operatorname{Re}(\lambda g_-g_+^*)\right].}
$$
The cross term is the <interference> between direct decay and decay after <Flavor eigenstate>[flavour] conversion. For reference, diagonal propagation gives $g_\pm=(e_\ell\pm e_h)/2$, where $e_j=e^{-im_jt-\Gamma_jt/2}$ and $t$ is <proper time>. The unfactored expression remains usable if $A_f=0$, when the ratio $\lambda$ itself is undefined.
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