How to convert an array of numbers into probability values?
Any Survival Function (1 minus the CDF) will have the desired property. Exponential is a potentially good candidate here, as it sometimes can be used to describe distances, but it's hard to say without more information.

$$S(x) = \exp(-ax)$$

The parameter $a$ can be tuned or possibly estimated from the data. 

For reference, if $a = 1$ then you get,

$$ [0.44, 0.58, 0.86]$$

$$[0.62, 0.4, 0.36]$$

for the first and second arrays respectively.