Sharper at Half the Temperature

A decoder-only model is continuing the text The sky is. For this problem its whole vocabulary is four tokens, and the scores it produces for them are

Sampling with temperature $T$ divides every score by $T$ before the softmax turns the scores into probabilities:

$p_i = \frac{e^{z_i / T}}{\sum_j e^{z_j / T}}$

The model itself is untouched — the four scores above are the same at every temperature. Only $T$ moves.

With $T = 0.5$, what probability does the model assign to blue?

Round your answer to 3 decimal places, and carry at least four decimals through the intermediate steps.