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.

Venus - Venus is Beauty, Desire and Love, Liquid Money. Venus is the main significator of marriage. Venus represents girlfriend or wife for a man. Venus is the significator of all relations, may it be husband-wife or mother-daughter. Philosophically speaking, Venus is also the cause of all the sufferings in our life. How? Because Venus represents our desires and we get pain and suffering in our life only when our desires are not fulfilled.

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 & Venus 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-Venus Conjunction - This is a conjunction where Venus is coming in contact with 2 strong fiery and hot planets. Venus is enemy to Sun and neutral to Mars but moreover, the basic nature of Venus doesn't match with basic nature of Sun-Mars. Venus is relationship, Sun is Ego and Mars is Dominance. To have a good relation, you have to let go of your ego. Also, if you want to have a long-lasting relationship then you can't be dominating in your relationship. Another way of looking at this conjunction is that if you want to keep your ego and dominance then your relation will suffer. And this is the end result of this conjunction. Relationship of person are deeply effected. Specially, if Venus is in between Sun and Mars degree-wise then it will work like a Paap Kartari Yoga and the gentle Venus will be crushed between 2 malefic planet. Although in beginning, person can be very passionate about the relation or about getting into relation but later relation can turn into more a dominance/ego battle. Positively, person can be working in financial field and will do anything to get a convenient an luxurious life. They can be in love of a pleasureful life. So again, Jeeva Karaka of Venus, i.e. relation/love/spouse will suffer due to presence of 2 strong malefic planets but person will still do good financially. 

Who will win the Conjunction? - Venus presence is almost negligible here and conjunction will depend on dignity of Sun & Mars. Whichever planet has better dignity will win the conjunction. 

Dignity & Strength - 

They will perform best in Sagittarius & Pisces where all 3 are in good dignity. In rest of the signs, the results will largely depend on the planet in better dignity or which planet is active as per dasha.