Candelabra

Fix one place to be a white candle. If there is another white candle next to it, the three black candles must all be adjacent, otherwise there will be a black candle between the two white candles. Since there are 4 places you could pick for your second white candle, and two of those are next to the first, the probability that all 4 black candles will be next to each other is 2/4=50%.

the number of ways of arrange in a linear way the candles is: - $\frac{5!}{2! \times 3 !} = 10$ - As the candles are arranged in a shaped cadelabra we must divide the result by 5, since we can just rotate the candles. The result is 2, so there are two ways, one with thre adjacent black candles and the other with only two.