Let's 1st understand what these planets represent on their own?

Sun - Sun represents Soul, Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.

Mars - Mars represents our will power, courage, ability to take actions, aggressive nature, anger, our fighting ability, brother, male friends, a boy friend for a girl, a soldier, an athlete and real estate etc.

Jupiter - It is the most benefic planet and it represents all the auspicious things like Knowledge, Wisdom, Law, Guru, Spirituality, Religion, Philosophy, Literature, Elderly People and Children etc. For a girl, Jupiter also represents Husband.

3 planetary conjunction - Whenever 3 or more planets are conjunct with each other in a house/sign then things related to that house/sign become a kind of life focus for person. It is because of huge accumulation of energy within 30 degrees of sky. It means not only these 3 planets' energy is going into this house/sign but the energy of at least 4 to 6 house/sign is going into this house/sign as these planets will be ruling some houses too. So, this house/sign with conjunction becomes almost the most important house in chart. During Career Consultation, I give a huge importance to any such house which has 3 or more planets in it.

House Ruler - Besides these karaka things, Sun, Mars & Jupiter will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include things related to the houses at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas.

Meaning of Sun-Mars-Jupiter Conjunction - This is a strong and a very good conjunction to have as all three planets are strong masculine benefic planets which are also mutual friends. If dignity is also good then this can be one of the most potent conjunction to give you success during its dasha. It is because the King (Sun), Minister (Jupiter) and Soldier (Mars) are aligned in their actions. There is no confusion between the person's purpose, belief and action. Person is very clear as to what he wants to achieve in life and acts towards it with all the positive intent. They all support and energize each other which can bring supreme authority for individual in his work field. This person can put lots of efforts in education. But where this conjunction can hurt is when person is given wrong beliefs and morale values from childhood. In that case, person follows those wrong moral values & beliefs and now actions will be towards protecting or projecting such wrong beliefs. This may show a religious fundamentalist too and in such cases because Sun-Mars are supporting those beliefs (Jupiter), you may find it almost impossible to make this person see other side of his beliefs. For him, his beliefs are always correct. So, good/bad result of this conjunction is always dependent on the dignity of planets. But overall, it is a good conjunction if person has a right purpose in life. 

Who will win the Conjunction? - All are strong masculine planets and will have equal say in this conjunction but whichever planet has better dignity sign-wise or active through dashas will have little higher say. 

Dignity & Strength - 

This conjunction can work best in Aries, Leo, Sagittarius and Pisces as Sun-Mars-Jupiter all are in good dignity here. 

In rest of the signs, at least 1 or 2 planets will be in weak dignity and result would depend on the planets with better dignity and dashas.