6. $\frac{17}{20}$.

It is easy to see that the rooms at the vertices are each adjacent to one room, the rooms on the sides of the large triangle (but not at the vertices) are each adjacent to two rooms, and the remaining rooms are each adjacent to three rooms. Therefore, the number of possible adjacent room pairs is
$$
\frac{1}{2}(3 \times 1 + 6 \times 2 + 7 \times 3) = 18.
$$

Thus, the required probability is $1 - \frac{18}{\mathrm{C}_{16}^{2}} = \frac{17}{20}$.
6. As shown in Figure 1, there are 16 small triangular rooms. Two people, A and B, are randomly placed in different small triangular rooms. The probability that they are in non-adjacent (do not share a common side) rooms is (expressed as a fraction).

保留源文本的换行和格式，翻译结果如下：

6. As shown in Figure 1, there are 16 small triangular rooms.  
Two people, A and B, are randomly placed in different small triangular rooms.  
The probability that they are in non-adjacent (do not share a common side) rooms is (expressed as a fraction).