Is there any mistake or am I missing something?
When I submit a probability vector P and another submission with vector 1-P, I got same AUC results. This did not come to right.
Also, the same problem occurs when I submit multiplying P vector with class prior probabilities. The values are totally different but accuracy is same.
there is no mistake. You may submit any type of scores, not only probabilities, thus a multiplication by a scalar does not change your result (only the order is important).
Moreover, the implementation of AUC used by the evaluation procedure does not require scores to sort the test objects by increasing chances of the occurrence of class '1' - also the decreasing ordering is checked, so AUC is always between 0.5 and 1.