Expected Softmax Classifier Output in CNN

Hi All,

What is the expected softmax classifier output during training the convolution neural network architecture under a supervised algorithm. So if we feed a dataset (let's say cifar-10), then we would expect to have one of 10 classes at the end of the network with probability close to 1 while the rest should be around zero. But the input dataset itself is a mix between cat images, dog images, etc. So I'm a little bit confused here, as all outputs from all the 10 classes should have probability close to one since we are training for all images.