4. Let's calculate the number of ways to write 3 digits:

$$
10 \cdot 10 \cdot 10=1000
$$

We will derive the formula for the number $A$, which is divisible by 5 and has a remainder of 3 when divided by 7. This number has the form

$$
A=5 k=7 n+3
$$

Solving the equation $5 k-7 n=3$ in integers, we find

$$
\left\{\begin{array}{l}
k=7 t+2 \\
n=5 t+1
\end{array}\right.
$$

Therefore, $A=35 t+10, t \in Z, t \geq 0$. Since by the problem's condition $A$ is a three-digit number, we have $100 \leq 35 t+10 \leq 999$. From this, taking into account the integer nature of $t$, we get $t=2,3, \ldots, 28$. This means that the number of three-digit numbers satisfying the problem's condition is 26. Therefore, the probability 
that a three-digit number divisible by 5 and having a remainder of 3 when divided by 7 can be seen on the table is $\frac{26}{1000}$.
Answer: $\quad P=0.026$.