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.

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. 

Rahu - It represents Illusion, Foreign Lands, Foreign Things (foreign as in unknown things. So, for someone living in Punjab, culture and rituals of Kerala is also unknown and hence Foreign), Drugs, Medicines, any type of intoxication, Fame, Wealth, Success, Obsession, Past-life incomplete Desires, Movies, Television, Online World, Cheating, Imagined Fears, Unusual Things, Unique Things, Creativity, Rule breaker. Rahu also blows things out of proportions. 

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, Saturn & Rahu 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-Saturn-Rahu Conjunction - As usually, one of the most stressful conjunction as 3 malefics coming together. This shows a person who has to struggle a lot initially in matters of career and finding his real path. It is always better for these people to work on their own because in career or even in normal walk of life they will automatically bump into those people who will hurt their ego. They will have real delay in prospering their Career and best results of their career can be seen in 40s. It is because Rahu is conjunct Saturn and hence delay of Saturn is furthe exploded which means huge delay in career. This conjunction can bring unpleasant events related with father in early life or it can be the case of almost no relation or association with Father. More so because not only that Sun is with its bitter enemy Saturn but this conjunction also shows that person was born during eclipse season. Hence, this person can grow up as fearful, timid and with lack of confidence because father was nowhere near to boost him up. So, they find their path with extreme delay. They can have this stage phobia or fear of authority or law. With authorities, they can have very stressful relation and if they decide to stay in job setup, it can be case of working whole life without any promotion or hike. Whichever house this conjunction may fall, things related to that house, especially Jeeva Karakas, are spoilt for almost whole life. Positively, they can be the most hardworking people on earth as Rahu will explode hard work trait of Saturn and person would have to work hard all the time as nothing will happen in life for them without putting their best efforts. 

Who will win the Conjunction? - Rahu is impacting both Sun & Saturn, hence Rahu is winning the conjunction. 

Dignity & Strength - 

In any sign/house, the results will be the same till mid 30s at least