As far as I'm aware a probability distribution only requires that some function $p(x)$ is non-negative over the reals, and integrates to unity.
If this is all it takes to define a probability distribution is it valid of me to normalise a likelihood function and call it a probability.
I have looked at the example from here:
where the integral of the given Bernoulli likelihood function is given to be 1/2.
If I then take this knowledge and divide this parameter (the 1/2 value) through my previous integral this will ensure that the likelihood function integrates to unity. However since the requirements for a valid probability distribution seem so relaxed (non-negative and integrate to unity), does this not mean I'm now dealing with a justifiably valid probability distribution? Or is there something else that I'm missing?