Determined by whom with what evidence? Sorry, you can't do probabilities without information.
Sorry, I was assuming you would be familiar with the arguments of fine tuning, and what presents the appearance of design in the universe etc. since I've had this discussion before with "SkepticThinker", " It Aint Necessarily So", "TagliattelliMonster" and others in various threads.
Apparently your not familiar with the old discussions.
I guess my main question was …Why choose one theory over another when neither has a proven cause? What pushes one towards a purposeless creation verses one purposefully created If the latter is a simpler explanation given certain observations?
As for the information you rightly asked for...some of what I considered would be, and I'll just quote some of the things I've said elsewhere in answer to others...
"Even assuming extremely favorable prebiotic conditions (whether realistic or not) and theoretically maximal reaction rates, such calculations have invariably underscored the implausibility of chance-based theories. These calculations have shown that the probability of obtaining functionally sequenced, information-rich biomacromolecules at random is, in the words of physicist Ilya Prigogine and his colleagues, "vanishingly small...even on the scale of...billions of years."
From: Prigogine, Nicolis, and Babloyantz, "Thermodynamics of Evolution,"23.
The probability of even a single functioning protein or corresponding functional gene by chance alone...stands at no better than 1 chance in 10^164.
From: Stephen Myer Calculations "The God Hypothesis"
"Chance" is an inadequate explanation for the origin of biological information
From: De Duve, "The Constraints of Chance"; Crick, Life Itself, 89-93
"Nobel laureate Christian de Duve, a leading origin-of-life biochemist until his death in 2013, categorically rejected the chance hypothesis precisely because he judged the necessary fortuitous convergence of events implausible in the extreme."
From: De Duve, "The Beginnings of Life on Earth," 437.
"...synthesizing (or maintaining) many essential building blocks or RNA molecules under realistic conditions has proven either difficult or impossible."
From: Shapiro, "Prebiotic Cytosine Synthesis."
"Hitching the components together in the right manner raises additional problems of such magnitude that no one has yet attempted to do so in a prebiotic context."
From: De Duve, Vital Dust, 23.
"...for every one DNA sequence that generates a short functional protein fold of just 150 amino acids in length, there 10^77 nonfunctional combinations-combinations that will not form a stable three-dimensional protein fold capable of performing a specific biological function."
From. Molecular biologist Douglas Axe. Established while working at the University of Cambridge Medical Research Council Lab from 1990 to 2003 using site-directed mutagenesis.
"In fact, if one considers the possible constants and laws that could have emerged, the odds against a universe that has produced life like ours are immense." Stephen Hawking, A Brief History of Time.
"Why did the universe start out with so nearly the critical rate of expansion that separates models that recollapse from those that go on expanding forever, that even now, 10 thousand million years later, it is still expanding at nearly the critical rate? If the rate of expansion one second after the Big Bang had been smaller by even one part in 100 thousand million million, the universe would have collapsed before it ever reached its present size." Ibid.
…"he showed (Roger Penrose) that there were 10^10^101 configurations of mass-energy that correspond to highly ordered universe like ours. But he had also shown that there were vastly more configurations 10^10^123 -- that would generate black-hole dominated universes. And since 10^10^101 is a minuscule fraction of 10^10^123, he concluded that the conditions that could generate a life-friendly universe are extremely rare …"
From: Penrose, "Time-Asymmetry and Quantum Gravity." aslo Penrose, The Road to Reality, 757-65; Gordon, "Divine Action and the World of Science," 259-61,267.
This by no means is an exhaustive representation of the arguments. Nor are the arguments conclusive of anything. I'm just interested in the discussion of such things.
I'm consistently getting the impression here that such impertinence, such arrogance, to even remotely bring into the conversation the possibility of purpose to creation is to be automatically met with derision instead of consideration. I don't understand that but would like to understand how that arises...or seems to.