Getting negative information gain with Laplace smoothing

Question

Is it possible to get negative information gain if Laplace smoothing is used too?

We know:

IG = H(Y) - H(Y|X)

Here, H is the entropy function and IG is the information gain.

Also:

H(Y) = -Σ_yP(Y=y).log₂(P(Y=y))

H(Y|X) = Σ_xP(X=x).H(Y|X=x)

H(Y|X=x) = -Σ_yP(Y=y|X=x).log₂(P(Y=y|X=x))

For example, suppose P(Y=y|X=x) = n_y|x/n_x. But it is possible that n_x = 0 and n_y|x = 0. So, I do laplace smoothing and define P(Y=y|X=x) = (n_y|x+1)/(n_x+|X|). Here, |X| denote the number of possible values that X can take(number of splits possible if X is chosen as the attribute). Is it possible that due to laplace smoothing, I get negative information gain?