I have the following probability distribution table:
[0.2, 0.3, 0.5]
I will then set the probability for event 1 to 0.
[0, 0.3, 0.5]
Now the question is what should the probabilities of the other events be, when everything has to add up to 1.
I'm not sure if its the first one or the second one?
[0, 0.375, 0.625] or [0, 0.4, 0.6]
Imagine throwing with a 3d die (only 3 sides) with probabilities [0.2, 0.3, 0.5] for throwing 1,2 and 3. Now we set the probability of throwing a 1 to zero. So it is only possible to throw a 2 and a 3.
Setting the probability of throwing a 1 to zero can be executed by throwing the die again until you throw a 2 or a 3. As the probability for throwing a 3 is larger than a 2, the increase of probability is also larger for 3 than for 2. So the probabilities are increased proportional to their original probabilities:
0.3:0.5 = x:(1-x)
From this we find x = 0.375 and 1-x = 0.625.
