Question 838663
52 cards, 13 Hearts, 39 Non-Hearts
First player - Heart
51 cards, 12 Hearts, 39 Non-Hearts
Look at the possible draws of the next three cards (H - heart, N - non-heart) and calculate the probabilities of each, they are all independent events.
NNN-{{{(39/51)(38/50)(37/49)=.438848}}}
NNH-{{{(39/51)(38/50)(12/49)=0.142329}}}
NHN-{{{(39/51)(12/50)(38/49)=0.142329}}}
NHH-{{{(39/51)(12/50)(11/49)=0.0412}}}
HNN-{{{(12/51)(39/50)(38/49)=0.142329}}}
HNH-{{{(12/51)(39/50)(11/49)=0.0412}}}
HHN-{{{(12/51)(11/50)(39/49)=0.0412}}}
HHH-{{{(12/51)(11/50)(10/49)0.010564}}}
If you sum up all of the probabilities, they do add up to 1. They must, these are the only possible draws.
Now look for the ones that have at least 1 heart. 
Or look for the one that has no hearts and subtract from 1.
P(at least 1 heart)={{{1-0.438848=0.561152}}}
Yes, all of them being hearts would be HHH, {{{P=0.010564}}}