Returning probabilities in a classification prediction in Keras?

So it turns out that the problem was I was not fully normalizing the data in the prediction script.

My prediction script should have had the following lines:

# these lines are copied from the example for loading MNIST data
(x_train, y_train), (x_test, y_test) = mnist.load_data()
x_train = x_train.reshape(60000, 784)
x_train = x_train.astype('float32') # this line was missing
x_train /= 255 # this line was missing too

Because the data was not cast to float, and divided by 255 (so it would be between 0 and 1), it was just showing up as 1s and 0s.

Keras predict indeed returns probabilities, and not classes.

Cannot reproduce your issue with my system configuration:

Python version 2.7.12
Tensorflow version 1.3.0
Keras version 2.0.9
Numpy version 1.13.3

Here is my prediction output for your x_slice with the loaded model (trained for 20 epochs, as in your code):

print(prev_model.predict(x_slice))
# Result: 
[[  1.00000000e+00   3.31656316e-37   1.07806675e-21   7.11765177e-30
    2.48000320e-31   5.34837679e-28   3.12470132e-24   4.65175406e-27
    8.66994134e-31   5.26426367e-24]
 [  0.00000000e+00   5.34361977e-30   3.91144999e-35   0.00000000e+00
    1.00000000e+00   0.00000000e+00   1.05583665e-36   1.01395577e-29
    0.00000000e+00   1.70868685e-29]
 [  3.99137559e-38   1.00000000e+00   1.76682222e-24   9.33333581e-31
    3.99846307e-15   1.17745576e-24   1.87529709e-26   2.18951752e-20
    3.57518280e-17   1.62027896e-28]
 [  6.48006586e-26   1.48974980e-17   5.60530329e-22   1.81973780e-14
    9.12573406e-10   1.95987500e-14   8.08566866e-27   1.17901132e-12
    7.33970447e-13   1.00000000e+00]
 [  2.01602060e-16   6.58242856e-14   1.00000000e+00   6.84244084e-09
    1.19809885e-16   7.94907624e-14   3.10690434e-19   8.02848586e-12
    4.68330721e-11   5.14736501e-15]
 [  2.31014903e-35   1.00000000e+00   6.02224725e-21   2.35928828e-23
    7.50006509e-15   4.06930881e-22   1.13288827e-24   4.20440718e-17
    4.95182972e-17   1.85492109e-18]
 [  0.00000000e+00   0.00000000e+00   0.00000000e+00   1.00000000e+00
    0.00000000e+00   6.30200370e-27   0.00000000e+00   5.19937755e-33
    1.63205659e-31   1.21508034e-20]
 [  1.44608573e-26   1.00000000e+00   1.78712268e-18   6.84598301e-19
    1.30042071e-11   2.53873986e-14   5.83169942e-17   1.20201071e-12
    2.21844570e-14   3.75015198e-15]
 [  0.00000000e+00   6.29184453e-34   9.22474943e-29   0.00000000e+00
    1.00000000e+00   3.05067233e-34   1.43097161e-28   1.34234082e-29
    4.28647272e-36   9.29760838e-34]
 [  4.68828449e-30   5.55172479e-20   3.26705529e-19   9.99999881e-01
    3.49577992e-22   1.27715460e-11   4.99185615e-36   1.19164204e-20
    4.21086124e-16   1.52631387e-07]]

I suspect some rounding issue when printing (or you have trained for much more epochs, and your probabilities for the training set have gotten very close to 1)...

To convince yourself that you indeed get probabilities and not class predictions, I suggest to try getting predictions from your model trained for a single epoch; normally you should see much less 1.0's - here is the case here for a model trained for epochs=1:

print(model.predict(x_slice))
# Result: 

[[  9.99916673e-01   5.36548761e-08   6.10747229e-05   8.21199933e-07
    6.64725164e-08   6.78853041e-07   9.09637220e-06   4.56192402e-06
    1.62688798e-06   5.23997733e-06]
 [  7.59836894e-07   1.78043920e-05   1.79073555e-04   2.95592145e-05
    9.98031914e-01   1.75839632e-05   5.90557102e-06   1.27705920e-03
    3.94643757e-06   4.36416740e-04]
 [  4.48473330e-08   9.99895334e-01   2.82608235e-05   5.33154832e-07
    9.78453227e-06   1.58954310e-06   3.38150176e-06   5.26260410e-05
    8.09341054e-06   3.28643267e-07]
 [  7.38236849e-07   4.80247072e-05   2.81726116e-05   4.77648537e-05
    7.21933879e-03   2.52177160e-05   3.88786475e-07   3.56770557e-04
    2.83472677e-04   9.91990149e-01]
 [  5.03611082e-05   2.69402866e-04   9.92011130e-01   4.68175858e-03
    9.57477605e-05   4.26214538e-04   7.66683661e-05   7.05923303e-04
    1.45670515e-03   2.26032615e-04]
 [  1.36330849e-10   9.99994516e-01   7.69141934e-07   1.44130311e-07
    9.52201333e-07   1.45219332e-07   4.43408908e-07   6.93398249e-07
    2.18685204e-06   1.50741769e-07]
 [  2.39427478e-09   3.75754922e-07   3.89349816e-06   9.99889374e-01
    1.85837867e-09   1.16176770e-05   1.89989760e-11   3.12301523e-07
    1.13220040e-05   8.29571582e-05]
 [  1.45760115e-08   9.99900222e-01   3.67058942e-06   4.04857201e-06
    1.97999962e-05   7.85745397e-06   8.13850420e-06   1.87294081e-05
    2.81870762e-05   9.38157609e-06]
 [  7.52560858e-09   8.84437856e-09   9.71140025e-07   5.20911703e-10
    9.99986649e-01   3.12135370e-07   1.06521384e-05   1.25693066e-06
    7.21853368e-08   5.21001624e-08]
 [  8.67672298e-08   2.17907742e-04   2.45352840e-06   9.95455265e-01
    1.43749105e-06   1.51766278e-03   1.83744309e-08   3.83995541e-07
    9.90309782e-05   2.70584645e-03]]