In Connectionist Temporal Classification (CTC), we assume that the output vectors in a single alignment sequence are conditionally independent given the input sequence. Mathematically, let the input sequence be $X=\{x_1, x_2, \dots, x_n\}$ where $x_i$ are vectors, and let the output alignment be $A=\{a_1, a_2, \dots, a_n\}$ where $a_i$ are vectors. Then, the conditional probability of the alignment given the input is $P_{CTC}(A|X)=\prod_{i=1}^{n}p(a_i|X)$.