Without such likelihoods, 'best explanation' collapses into 'only theistic explanation considered,' which is a fallacy of incomplete alternatives rather than genuine abductive inference.

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abductive inference(Peirce's revised taxonomy of inference types): A class of probable inference distinct from induction, also called hypothesis or retroductive inference by Peirce
best explanation(Thomson's inference from cathode ray experiments): The most plausible — and in this case presumably the only plausible — account of a set of experimental results, adopted as a conclusion in the absence of logical entailment or statistical data
fallacy of incomplete alternatives(as a type of faulty reasoning): A logical error where you conclude something is true just because you haven't considered all other possible explanations.
likelihoods(Bayesian confirmation theory): The probability of the evidence given a particular hypothesis, used in conjunction with prior probabilities to determine expectedness

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