If the prior is not mentioned, as you supposed, it is assumed uniform (constant).

Thus the posterior is a density that is $\propto$ likelihood....

The symbol $\propto$ means that to ensure that your posterior is a nice density you have to normalize the likelihood....

Here is an example.

Draw a coin (we do not know if it is fair or not) 10 times getting 6 Heads and 4 Tails.

As we do not know anything about the "fair or not fair" parameter $\theta$ the posterior is

$$\pi(\theta|\mathbf{x}) \propto \theta^6 (1-\theta)^4$$

(in the likelihood we do not consider the constant $\binom{10}{6}$ because it is independent from $\theta$ so it doesn't give us any useful information)

It is understood that, to ensure that $\pi(\theta|\mathbf{x})$ is a density we have to normalize the likelihood (observed likelihood) finding

$$\pi(\theta|\mathbf{x})=2310\cdot \theta^6 \cdot(1-\theta)^4$$

I do not quite understand the problem statement which is in terms of "normalized likelihoods".

If the prior is not mentioned, as you supposed, it is assumed uniform (constant).

Thus the posterior is a density that is $\propto$ likelihood....

The symbol $\propto$ means that to ensure that your posterior is a nice density you have to normalize the likelihood....

Here is an example.

Draw a coin (we do not know if it is fair or not) 10 times getting 6 Heads and 4 Tails.

As we do not know anything about the "fair or not fair" parameter $\theta$ the posterior is

$$\pi(\theta|\mathbf{x}) \propto \theta^6 (1-\theta)^4$$

(in the likelihood we do not consider the constant $\binom{10}{6}$ because it is independent from $\theta$ so it doesn't give us any useful information)

It is understood that, to ensure that $\pi(\theta|\mathbf{x})$ is a density we have to normalize the likelihood (observed likelihood) finding

$$\pi(\theta|\mathbf{x})=2310\cdot \theta^6 \cdot(1-\theta)^4$$