Odds of successive outcomes with weighted probabilities

Hello, I am a statistics and probabilities novice and I'm having trouble with this problem. I'll lay out an example:

Team A and team B are playing each other. Team A has lost 4 games in a row with probabilities of winning the individual games as follows:

Team A 4-game losing streak (individual winning probabilities):
1. 38.6%
2. 43.6%
3. 40%
4. 48%

On the other hand, team B comes into the game on a 3-game winning streak, their odds of winning those 3 games were as follows:

Team B 3-game winning streak (individual winning probabilities):
1. 58.3%
2. 62%
3. 53.9%

Given these streaks what are the probabilities of each team winning this game based solely on bucking these improbable streaks?