If you normalise a likelihood function, does it become a valid and probability distribution. [duplicate]

This question already has an answer here:

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:

What is the reason that a likelihood function is not a pdf?

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?

marked as duplicate by Xi'an, kjetil b halvorsen, mdewey, Michael Chernick, JohnFeb 15 '17 at 4:14

• If $\int p(x)\,\text{d}x <\infty$, you can turn $p$ into a probability density. Which meaning can you associate with this probabilistic object? In which sense is it justified or valid? – Xi'an Feb 14 '17 at 11:59