Why binary classification with highly imbalanced dataset output low probs? I'm doing a frauds detection project which is using imbalance dataset(almost, 9:1).
And I using logistic, xgboost, and ligthgbm for Binary Classification.
When I predict my test set, I see all of Target's probabilities are so low.
Is it wrong for my models? or Is it natural for imbalanced case?

Fraud is an uncommon event. Even when some signs of fraud are there, the odds are that the transaction was legitimate. Unless something is screaming at you, the probability of fraud would be low. Consequently, you might not demand a high probability to flag a case as potential fraud.
The class imbalance reflects the fact that fraud is uncommon. You can see how this impacts your predicted probability if you write out Bayes’ theorem with your predicted probability as the posterior probability of fraud, given the data, and the class ratio as the prior.
$$
P(Fraud\vert Features)=\dfrac{
P(Features\vert Fraud)P(Fraud)
}{
P(Features)
}
$$
$P(Fraud\vert Features)$ is called the "posterior probability" of fraud. $P(Fraud)$ is called the "prior probability" of fraud and is equal to the proportion of cases that are fraud.
When the $P(Fraud)$ in the numerator is low, of course the other side of the equation will be low.
