Why for the same z-score, the left probability is different from 1-right probability? I'm doing an exercise, and I come up with a z-score = 2/3 (or 0.66). Which in the left tail of the z-table here it's equivalent to a probability of 0.7454 and for the right tail of the table is a probability of 0.2454.
Why the 1 - right probability is different from the left probability? In other words, why:
1-0.2454 = 0.7546 <> 0.7454 ? What are the decimals I'm missing?
 A: 
You better look at this image very carefully. Just as your post shares: This z-table (normal distribution table) shows the area to the right-hand side of the curve. Use these values to find the area between z=0 and any positive value. For an area in a left tail, look at this left-tail z-table instead.
In other words, the right-tail side is being represented by the area under the curve to the right of the yellow region while the left-tail side the left.
The sum of left & right tails should be lower than 1.
A: The two values aren't meant to sum to 1. Rather, the difference between them is meant to be 0.5. This is because half of the probability mass is to the left of the mean.
Quoting the article you linked:

Sometimes you’ll want to know the area between the mean and some positive value. That’s when you’ll use the right-hand z-table. But other times you might want to know the area in a left tail. If that’s the case, use the z-table that shows the area to the left of z.

Your left-hand value is the integral of a standard normal PDF from $-\infty$ to your $z$-value. Your right-hand value is the integral of a standard normal PDF from $0$ to your $z$-value.
