Probability certain class is the biggest in multinomial distribution

Question

Suppose we have a multinomial distribution: $$Pr(X_1 = x_1, X_2 = x_2, \dots, X_k = x_k)=\dfrac{n!}{x_1! x_2! \cdots x_k!} \cdot p_1^{x_1}\cdot p_2^{x_2} \cdots p_k^{x_k}$$

What is the probabilty that $X_1=max(X_1,X_2,X_3,\dots,X_k)$ ?