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.

Saturn - It is all that which we don't like in our life. Saturn is Delay, Frustration, Restriction, Limitation and Anxiety. It is people of Authority, like Boss at your Work Place or Father-Figure at Home. Saturn is our Karmic Debt from past-life. Saturn is the things we didn't treat too well in our past life. Saturn is our Challenges and Lessons of life. Saturn is Old-Age, Teeth/Bones in Human Body, Diseases, Changes etc. Saturn represents our Step-Relations, it means that wherever Saturn sits, people related with that house give us Step Treatment. Saturn is Hard Work, Efforts and most importantly Perseverance etc. Nothing comes easy and in one go with Saturn. You have to work hard continuously over the longest possible period of life. Saturn makes a person Legend as Legends have one thing in common that they choose one field and work hard in it for whole life. 

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 & Saturn 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-Saturn Conjunction - This is one of the many stressful conjunctions which we talk about when all malefic planets come together. Sun-Mars are with their mutual enemy Saturn. It makes this conjunction as very stressful specially for the things related to the house where it is falling. Person may get results related to that house only after mid-30s. This conjunction can also make someone very fearful and afraid because confidence (Sun) and Courage (Mars) are seriously impacted by Fear (Saturn). It also makes them fearful of law and authority figures. The relation with Father and Brother or other male friends will be equally stressful and challenging as Saturn is going to put restrictions there. Any progress in Career and favorable results of actions will be delayed till 30s. But what this makes is a very hardworking person because nothing is going to come easy for them. As they are fearful of law, actually it can make them extremely law abiding and disciplined person. They have to put their best effort for the longest period of time to gain anything. This conjunction can take them in Govt field or Law related field. As they are Law abiding people, so they become protector of Law. 

Who will win the Conjunction? - Saturn's involvement in conjunction ensures that Saturn will have the final say in results of this conjunction. 

Dignity & Strength - As Saturn is involved, results will be more or less same in every house/sign.