How to derive likelihood of an event from probability values? What's the difference/relation between odds and likelihood? I am trying to understand the relationship between probability, odds, logit values and likelihood. Is there any?
 A: Let's assume we have a probability distribution $f(x)$. $f(x)dx$ is the probability that we draw a value that lies in small area around $x$. Typically, our probability distribution has a number of parameters that define it (for example, for normal distribution that will be mean $
\mu$ and variance $\sigma$). Let's wrap all of those parameters inside vector $\theta = (param1, param2, ..., paramN)$. Then our distribution formula will look like this: $f(x, \theta)$. When we calculate probabilities for our distribution we think of $f(x, \theta)$ as if $\theta$ were fixed (we know our parameters when we try to calculate probabilities) and $x$ were varying (we calculate probabilities for values $x$ that we substitute in the probability density function). 
When we shift our view and think of $\theta$ as varying and $x$ as fixed we are getting likelihood function instead of probability density function. I will denote that as $L(\theta | x)$ (reads as "likelihood of  $\theta$ given $x$"). For what purpose do we need that? Typically, to estimate distribution's parameters by given values of $x$ (those were drawn from the distribution with unknown parameters).
Now, lets imagine we have two candidates for our parameters - $\theta_1$ and $\theta_2$. How do we know which of them is more favorable? If we divide one by another we will compute likelihood odds ratio 
$$
\Lambda = \frac{L(\theta_1 | x)} {L(\theta_2 | x)}
$$
