In this paper, we study the transmit signal optimization in a multiple-input multiple-output (MIMO) radar system for sensing the angle information of multiple targets via their reflected echo signals. We consider a challenging and practical scenario where the angles to be sensed are unknown and random, while their probability information is known a priori for exploitation. First, we establish an analytical framework to quantify the multi-target sensing performance exploiting prior distribution information, by deriving the posterior Cramér-Rao bound (PCRB) as a lower bound of the mean-squared error (MSE) matrix in sensing multiple unknown and random angles. Then, we formulate and study the transmit sample covariance matrix optimization problem to minimize the PCRB for the sum MSE in estimating all angles. Moreover, we propose a sum-of-ratios iterative algorithm which can obtain the optimal solution to the PCRB-minimization problem with low complexity. Numerical results validate our results and the superiority of our proposed design over benchmark schemes.