Let red marbles be presented with R and black marble with B. Also, let E be the event that at least one of the three marbles drawn be black when the first marble is red.

Now, the following three conditions are possible, if atleast one of the three marbles drawn be black and the first marble is red.

(i)  \[{{E}_{1}}:{{2}^{nd}}\] ball is black and \[{{3}^{rd}}\] ball is red

(ii) \[{{E}_{2}}:{{2}^{nd}}\] ball is black and \[{{3}^{rd}}\] ball is also black

(iii) \[{{E}_{3}}:{{2}^{nd}}\]  ball is red and \[{{3}^{rd}}\] ball is black

The probabilities of the above events are:

Therefore, the required probability is \[25/56\].