MIS weights for BDPT are calculated with ratios of PDFs for each vertex under different types of light transport (radiance vs. importance). These probabilities are regenerated for frontier vertices during subpath connection, which makes sense - the direction from the $t-1$-th camera vertex to the $s-1$-th light vertex will be different to the direction between the $t-1$-th and $t$th camera vertices.
PBRT also reccomends updating reverse probabilities for previous vertices, though. Why? The probability of tracing a ray from $s-1$ to $s-2$ won't be affected by the probability of tracing a ray between $s-1$ and $t-1$.