Each tile can be black, white, or grey, giving a probability of \(\frac{1}{3}\) for each color. To ensure no two adjacent tiles are the same color, the first tile can be any color, but each subsequent tile must be a different color from the one before it.

For each of the 7 subsequent tiles, there are 2 choices (not the same as the previous tile), so the probability for each is \(\frac{2}{3}\).

The total probability is:

\(\left( \frac{2}{3} \right)^7 = \frac{128}{2187}\)

Thus, the probability that no two adjacent tiles are the same color is \(\frac{128}{2187}\) or approximately 0.0585.