how to interpret a conditional probability

I wonder if you could help me and point me to somewhere.

this is a simple question (I think), but not for me.

Say, you estimated a conditional probability

P(theta_1 | x) = 0.54,

THETA = {theta_1, theta_2}, wehre P(theta_1)=P(theta_2)=0.5.

So, Theta is dichotomous (yes, no), x is data/observation, and the prior

probabilities are 0.5. This conditional probability means that after

observation x, the probability of P(theta_1 | x) improved only slightly

(compared to the prior P(theta_1) = 0.5).

How do you evaluate this conditional probability? Any index to say

something statistically? For example, you can caculate the posterior odds
for theta_1;

0.54/(1-0.54) or take the logorithm of the odds. Then, how do you evaluate

these statistically? Is there any way to evluate how much 0.54 is

informative (statistically)? where should I look?

Thank you

takashi


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