Is the concept of cosmological design independent from biological intelligent design, or does one phenomenon increase the probability of the other?

By the law of total probability, we can formulate the probability of biological intelligent design, P (BID), as a sum of conditional probabilities weighted by the probability of cosmological intelligent design, P (CID). Here is the equation:

P (BID) = P (BID | CID) * P (CID) + P (BID | not CID) * P (not CID)

From arguments invoking fine-tuning and other orderly aspects of the universe (and even the Privileged Planet Hypothesis), it is reasonable to think that P (CID) is not low. I get the feeling that the notion of cosmological intelligent design is generally more accepted than biological intelligent design.

The next probability to consider is P (BID | CID). How likely is biological intelligent design given that cosmological intelligent design is true? If the universe were designed in such a way to make life possible, would not the design extend to the biological realm? After all, it seems like the end goal of the cosmological design is life. In other words, if the universe's constants were designed for life, then it would also make sense for life itself to be designed, rather than letting life arise by abiogenesis through purely natural stochastic processes. Thus, P (BID | CID) is indeed quite high. It is quite probable for design at the cosmological scale to cascade down to design at the biological realm.

I will not analze the other term in the summation, for that term can only increase P (BID):

P (BID) > P (BID | CID) * P (CID)

The two probabilities on the right hand side are quite high, by the reasoning in the previous paragraphs:

P (BID) > "sufficiently high probability" * "sufficiently high probability"

The product of two sufficiently high probabilities is still a pretty reasonable probability (e.g. 0.6 * 0.6 = 0.36). Therefore, biological intelligent design has at least a reasonable probability:

P (BID) > "reasonable probability"