You got this line because your data are stored in an histogram. Therefore with option line L, C etc … all the bins are drawn, even the empty ones. To draw only a line through the few points you have, the simplest would be to use a TGraph and draw it on top of the histogram using option L. Do you know how to put these few points in a TGraph ?
Also, an other simple solution could be to set the histogram minimum to 0.