A condition for transitivity in probabilistic support

It is well known that probabilistic support is not transitive. But it can be shown that probabilistic support is transitive provided the intermediary proposition screens off the original evidence with respect to the hypothesis in question. This has the consequence that probabilistic support is transitive when the original evidence is testimonial, memorial or perceptual (i.e., to the effect that such and such was testified to, remembered, or perceived), and the intermediary proposition is its representational content (i.e., to the effect that the such and such occurred).