I'm not quite sure what OP thinks base64 means, but:
> the probability that changeme is actually valid base64 encoding must be very low
This makes no sense. The characters are part of the base64 alphabet and you have an acceptable number of them.
You wouldn't claim that the probability that deadbeef is a valid base 16 number must be very low. Probability doesn't come into it, the characters are part of the alphabet, that's all there is to it.
> the probability that changeme is actually valid base64 encoding must be very low
This makes no sense. The characters are part of the base64 alphabet and you have an acceptable number of them.
You wouldn't claim that the probability that deadbeef is a valid base 16 number must be very low. Probability doesn't come into it, the characters are part of the alphabet, that's all there is to it.