Probability applies to chance events. Purposeful design is not chance so it is not that one can't determine the probability of purposeful design, it just makes no sense to speak of it that way.
Why not? You could set up an experiment giving a disparate set of individuals the same task, say, designing a paper airplane that will fly 20'. You could separate them by age, or occupation, or species or whatever and use the information gained to calculate the probabilities of a certain individual performing the design function.
There is uncertainty in the results or performance of a design against the intended function but it makes no sense to speak of the probability of design.
You have to know something of capabilities and process to determine if there were
intended function. Even the definitions are inadequate: I suppose Design is
an intentional arrangement of parts and I guess you would define Intelligence as an
capable of thinking like a human. It's not helpful. Even a functional design can happen by accident - unintended design. Or by a combination of design and chance. Without knowlege of intent and process the whole concept of Intelligent Design is useless.
This is why the method is "Chance Elimination". One looks at the probability that the event could have been generated by the set of chance hypotheses but not the design hypotheses.
No fair. In assessing which hypothesis is more probable you have to weigh the design hypothesis against the current evolutionary hypothesis. Evolution has the observed phenomenon of selection and genetic drift operating through a process of genetic recombination. Every fossil found, every
genetic history teased out, every regulatory gene/phenotype interaction changes the probabilities of the evolutionary hypothesis. Without a proposed process or even an identified timeline for a designed feature you can't begin to make a comparison as to whether evolution or design is more likely. Until you come up with some empirical design evidence the most likely explanation for biological diversity is the evolutionary hypothesis. If you feel that you have proved to your own satisfaction that the current evolutionary synthesis is statistically inadequate to explain the present diversity of life then the default is don't know. And to be considered science "don't know" will always default to some testable naturalistic hypothesis.