Interpretation of likelihood ratio and hypothesis testing

Even after extensive search, am unclear on some (basic) concepts regarding likelihood vs. frequentist approach in hypothesis testing. Can you please help? Here we go:

Suppose I have observed an outcome O, and I know that a parameter θ has influence on the outcome and can acquire two (and only two) discrete values: θ1 or θ2.

Suppose further that P(O| θ1) = c . P(O| θ2)

and therefore L(θ1 | O) = c . L(θ2 | O)

If my set of hypotheses are:

H1: θ = θ1
H2: θ = θ2

which of these statements, if any, can I make?

• H1 is c-times more likely to be true than H2 ?
• If I choose H1 , I will be wrong 100/(c+1) % of times?
• If I choose H1 , I have a 100/(c+1) % chance of being wrong?

Thank you for your time.