Considerations for choosing the correct hypothesis

How do you calculate the probability for each?
Let's say the probability that I assume a machine is random is 80% and the probability that it is designed is 20%.
The probability of getting a black ball is 10^-6
Is there some formula to calculate what I should choose?

Assuming that the machine is designed to choose a red ball with certainty (there are other possibilities, of course), then you must calculate a conditional probability.
A – A machine is designed.
B – Not designed.
You have given the basic probabilities:
P(A), P(B)
: The conditional probabilities for the event that a red ball is drawn are:
P(X/A) = 1
P(X/B) = 1/1000000
Now you must calculate, using Bayes' complete probability formula, the inverse conditional probabilities:
P(A/X), P(B/X)
, and comparing them gives you the answer.

Here it is clear even without calculation that it is designed with a very high probability.

I don't know the formula but I put it according to Wikipedia and that's how I did it
(0.8/1000000 + 0.2 ) / 0.2
The result is 0.999996 and according to the second one it came out 0.00000399

Does that make sense?

Absolutely. That's exactly the result.

So on the side that the universe has a universe and dualism is distilled to explain.
The chance that such a universe will come about randomly (according to the Stanford Encyclopedia) is 229-^10

The chance that such a universe will come about programmed is 1

As long as you see the hypothesis that there is a God as more possible and plausible than 9.9*10^-228 you should assume that there is a God in 99%
 x/(x+(1-x)/​(1e+229))=0.99
X=9.9*10^-228
Am I right?

Beyond the numbers, which are nonsense of course, the argument is correct. This is called the physico-theological evidence and I have expanded on it in my notebooks here on the site.